Does uninstalling Steam also uninstall games installed through steam?

Move the subfolder /steamapps/ in a safe place before uninstalling Steam, then do the following steps:

1. Uninstall Steam
2. Reinstall Steam
3. Launch Steam
4. Exit Steam
5. Move the content of your /steamapps/ backup to the new /steamapps/ subfolder
6. Relaunch Steam

At this point Steam should find all games without any other action; in the worst case, where Steam does not detect some games as installed, just reinstall them and the game will be downloaded and ready in few seconds/minutes because it only need to validate the game content cache.

You can also create a backup of your Steam Games. You can use it to backup your saves to CD, DVD or an external hard drive. You also have the option of backing up individual games or all of your Steam games. If you backup multiple games at once, you are given the option to choose which games you'd like to restore when you initiate the restore procedure. I used this when upgrading from Windows Vista to Windows 7.

See Steam Support:Using the Steam Backup Feature

Before drilling a giant hole through the mountain, you can check if there are pathways around it.

Have you tried deleting everything except your steam.exe and steamapps in the same directory and re-running steam.exe?