You do not need to uninstall your games to re-install Steam. A typical way to "repair" Steam is to delete everything in C:\Program Files (x86)\SteamEXCEPT the SteamApps folder (where the game files are) and the Steam.exe. Once all of that is deleted, running Steam.exe will redownload all of the program files and everything will be like new.
If this does not work then you should re-install Steam the proper way. It still shouldn't remove your games.