You may need to reinstall the locally installed files that Minecraft puts into place. To do so, press your Windows+R keys, type in %AppData% at the dialog, and press Enter. In the window that appears, open the .minecraft directory, and delete everything except for the saves directory that you see therein.
Next, go to Control Panel, and click on "Uninstall a Program" (may also be called "Programs and Features"). Then, right click on the Minecraft entry and select "Uninstall". Afterwards, restart your PC, then download and run the .msi at https://minecraft.net/en-us/download. Then, try running Minecraft again.
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