I am getting the same error even after dowloading the fix from WithinWindows this is the erro message i get Bad video card drivers!
Minecraft was unable to start because it failed to find an accelerated OpenGL mode.
This can usually be fixed by updating the video card drivers.
--- BEGIN ERROR REPORT 7fe0271 --------
Generated 31-1-13 12:42
-- System Details --
Minecraft Version: 1.4.7
Operating System: Windows 8 (x86) version 6.2
Java Version: 1.7.0_11, Oracle Corporation
Java VM Version: Java HotSpot(TM) Client VM (mixed mode), Oracle Corporation
Memory: 425459008 bytes (405 MB) / 518979584 bytes (494 MB) up to 1037959168 bytes (989 MB)
JVM Flags: 2 total; -Xms512m -Xmx1024m
AABB Pool Size: 0 (0 bytes; 0 MB) allocated, 0 (0 bytes; 0 MB) used
Suspicious classes: No suspicious classes found.
IntCache: cache: 0, tcache: 0, allocated: 0, tallocated: 0
OpenGL: ~~ERROR~~ NullPointerException: null
Is Modded: Probably not. Jar signature remains and client brand is untouched.
Type: Client (map_client.txt)
Texture Pack: Default
Profiler Position: N/A (disabled)
Vec3 Pool Size: ~~ERROR~~ NullPointerException: null[failed to get system properties (java.lang.NullPointerException)]
org.lwjgl.LWJGLException: Pixel format not accelerated
at org.lwjgl.opengl.WindowsPeerInfo.nChoosePixelFormat(Native Method)
at java.lang.Thread.run(Unknown Source)
--- END ERROR REPORT e481b738 ----------
The problem is that you most likely don't have the needed drivers for your machine; AMD has legacy drivers if your machine is running a Radeon HD 2000, 3000, or 4000 Series card. You can find the legacy drivers here. I had the exact same issue as you (pixel format not accelerated), and installing these legacy drivers solved it.
Also, Mikko_blu, how would updating LWJGL help if he's getting the error "Minecraft was unable to start because it failed to find an accelerated OpenGL mode. This can usually be fixed by updating the video card drivers."? Sorry if I'm incorrect, but I don't think updating LWJGL would ever help with that (the latest version of LWJGL has a flaw there you can't use your mouse button and keyboard keys at the same time, anyways).