Tried through Firefox again, so I went through the console and realized I must have been looking at the wrong data before. Here's the entire output. (I snipped out my name, password and proxy address.

)
security: property package.access value sun.,com.sun.xml.internal.ws.,com.sun.xml.internal.bind.
security: property package.access new value
sun.,com.sun.xml.internal.ws.,com.sun.xml.internal.bind.,com.sun.javaws
security: property package.access value
sun.,com.sun.xml.internal.ws.,com.sun.xml.internal.bind.,com.sun.javaws
security: property package.access new value
sun.,com.sun.xml.internal.ws.,com.sun.xml.internal.bind.,com.sun.javaws,com.sun.deploy
security: property package.access value
sun.,com.sun.xml.internal.ws.,com.sun.xml.internal.bind.,com.sun.javaws,com.sun.deploy
security: property package.access new value
sun.,com.sun.xml.internal.ws.,com.sun.xml.internal.bind.,com.sun.javaws,com.sun.deploy,com.sun.jnlp
security: property package.definition value null
security: property package.definition new value com.sun.javaws
security: property package.definition value com.sun.javaws
security: property package.definition new value com.sun.javaws,com.sun.deploy
security: property package.definition value com.sun.javaws,com.sun.deploy
security: property package.definition new value com.sun.javaws,com.sun.deploy,com.sun.jnlp
security: property package.access value
sun.,com.sun.xml.internal.ws.,com.sun.xml.internal.bind.,com.sun.javaws,com.sun.deploy,com.sun.jnlp
security: property package.access new value
sun.,com.sun.xml.internal.ws.,com.sun.xml.internal.bind.,com.sun.javaws,com.sun.deploy,com.sun.jnlp,org.mozi
lla.jss
security: property package.definition value com.sun.javaws,com.sun.deploy,com.sun.jnlp
security: property package.definition new value com.sun.javaws,com.sun.deploy,com.sun.jnlp,org.mozilla.jss
network: Cache entry not found [url]
network: Connecting http://minecraft.net/ with proxy=HTTP @ myproxy/proxyurl:proxyport
network: Connecting http://minecraft.net/ with cookie
"information, including my login and password"
network: Cache entry found [url]
network: Connecting http://minecraft.net/client/lwjgl_util_applet.jar with proxy=HTTP @
myproxy/proxyurl:proxyport
network: Connecting http://minecraft.net/client/lwjgl_util_applet.jar with cookie
"information, including my login and password"
network: ResponseCode for http://minecraft.net/client/lwjgl_util_applet.jar : 304
network: Encoding for http://minecraft.net/client/lwjgl_util_applet.jar : null
network: Disconnect connection to http://minecraft.net/client/lwjgl_util_applet.jar
security: Accessing keys and certificate in Mozilla user profile: null
security: Loading Root CA certificates from C:\Program Files\Java\jre6\lib\security\cacerts
security: Loaded Root CA certificates from C:\Program Files\Java\jre6\lib\security\cacerts
security: Loading Deployment certificates from C:\Documents and Settings\myname\Application
Data\Sun\Java\Deployment\security\trusted.certs
security: Loaded Deployment certificates from C:\Documents and Settings\myname\Application
Data\Sun\Java\Deployment\security\trusted.certs
security: Loading certificates from Deployment session certificate store
security: Loaded certificates from Deployment session certificate store
security: Validate the certificate chain using CertPath API
security: Obtain certificate collection in Root CA certificate store
security: Obtain certificate collection in Root CA certificate store
security: No timestamping info available
security: Found jurisdiction list file
security: No need to checking trusted extension for this certificate
security: The CRL support is disabled
security: The OCSP support is disabled
security: Checking if certificate is in Deployment denied certificate store
security: Checking if certificate is in Deployment permanent certificate store
basic: Applet loaded.
basic: Applet resized and added to parent container
basic: PERF: AppletExecutionRunnable - applet.init() BEGIN ; jvmLaunch dt 266685 us, pluginInit dt 1172812
us, TotalTime: 1439497 us
network: Cache entry found [url]
network: Connecting http://minecraft.net/client/lzma.jar with proxy=HTTP @
myproxy/proxyurl:proxyport
network: Connecting http://minecraft.net/client/lzma.jar with cookie
"information, including my login and password"
network: ResponseCode for http://minecraft.net/client/lzma.jar : 304
network: Encoding for http://minecraft.net/client/lzma.jar : null
network: Disconnect connection to http://minecraft.net/client/lzma.jar
network: Cache entry not found [url]
network: Connecting http://minecraft.net/client/logo_small.png with proxy=HTTP @
myproxy/proxyurl:proxyport
network: Connecting http://minecraft.net/client/logo_small.png with cookie
"information, including my login and password"
security: Loading certificates from Deployment session certificate store
security: Loaded certificates from Deployment session certificate store
security: Validate the certificate chain using CertPath API
security: Obtain certificate collection in Root CA certificate store
security: Obtain certificate collection in Root CA certificate store
security: No timestamping info available
security: Found jurisdiction list file
security: No need to checking trusted extension for this certificate
security: The CRL support is disabled
security: The OCSP support is disabled
security: Checking if certificate is in Deployment denied certificate store
security: Checking if certificate is in Deployment permanent certificate store
basic: Applet initialized
basic: Applet made visible
basic: Starting applet
basic: Applet started
basic: Told clients applet is started
java.io.EOFException: Unexpected end of ZLIB input stream
at java.util.zip.InflaterInputStream.fill(Unknown Source)
at java.util.zip.InflaterInputStream.read(Unknown Source)
at java.io.BufferedInputStream.fill(Unknown Source)
at java.io.BufferedInputStream.read(Unknown Source)
at sun.awt.image.PNGImageDecoder.produceImage(Unknown Source)
at sun.awt.image.InputStreamImageSource.doFetch(Unknown Source)
at sun.awt.image.ImageFetcher.fetchloop(Unknown Source)
at sun.awt.image.ImageFetcher.run(Unknown Source)
security: Loading certificates from Deployment session certificate store
security: Loaded certificates from Deployment session certificate store
security: Validate the certificate chain using CertPath API
security: Obtain certificate collection in Root CA certificate store
security: Obtain certificate collection in Root CA certificate store
security: No timestamping info available
security: Found jurisdiction list file
security: No need to checking trusted extension for this certificate
security: The CRL support is disabled
security: The OCSP support is disabled
security: Checking if certificate is in Deployment denied certificate store
security: Checking if certificate is in Deployment permanent certificate store
security: Loading certificates from Deployment session certificate store
security: Loaded certificates from Deployment session certificate store
security: Validate the certificate chain using CertPath API
security: Obtain certificate collection in Root CA certificate store
security: Obtain certificate collection in Root CA certificate store
security: No timestamping info available
security: Found jurisdiction list file
security: No need to checking trusted extension for this certificate
security: The CRL support is disabled
security: The OCSP support is disabled
security: Checking if certificate is in Deployment denied certificate store
security: Checking if certificate is in Deployment permanent certificate store
security: Loading certificates from Deployment session certificate store
security: Loaded certificates from Deployment session certificate store
security: Validate the certificate chain using CertPath API
security: Obtain certificate collection in Root CA certificate store
security: Obtain certificate collection in Root CA certificate store
security: No timestamping info available
security: Found jurisdiction list file
security: No need to checking trusted extension for this certificate
security: The CRL support is disabled
security: The OCSP support is disabled
security: Checking if certificate is in Deployment denied certificate store
security: Checking if certificate is in Deployment permanent certificate store
network: Cache entry not found [url]
network: Connecting http://www.minecraft.net/resources/ with proxy=HTTP @
myproxy/proxyurl:proxyport
network: Connecting http://www.minecraft.net/resources/ with cookie
"information, including my login and password"
basic: unique id: com_sun_deploy_AboutJava-6.0
basic: server port at: 4384
basic: getSingleInstanceFilename: C:\Documents and Settings\myname\Application
Data\Sun\Java\Deployment\tmp\si\com_sun_deploy_AboutJava-6.0-x86_4384
basic: waiting connection
network: Connecting http://127.0.0.1:4384/ with proxy=DIRECT
basic: recv: javaws.singleinstance.stop
basic: getSingleInstanceFilename: C:\Documents and Settings\myname\Application
Data\Sun\Java\Deployment\tmp\si\com_sun_deploy_AboutJava-6.0-x86_4384
basic: getSingleInstanceFilename: C:\Documents and Settings\myname\Application
Data\Sun\Java\Deployment\tmp\si\com_sun_deploy_AboutJava-6.0-x86_4384
basic: removed SingleInstanceFile: C:\Documents and Settings\myname\Application
Data\Sun\Java\Deployment\tmp\si\com_sun_deploy_AboutJava-6.0-x86_4384
It certainly looks like it's trying to connect through the proxy, nor do I see any weird errors.