Sounds kind of serious, from personal experience with programs going wacky:
>Before trying to start the program check your Task Manager in the processes tab for lolclient.exe and/or lollauncher.exe; if either of these are present without your input, end the processes, watch the Manager for a few seconds to see if anything happens and try launching the game.
Uninstalling everything using add/remove programs, then search for any folders left in C:\\Riot Games\ or in the hidden AppData folder in the Users section of your C drive, delete those as well, then go into the registry and delete any entries orphaned from the uninstallation that was just performed. [An easier way to remove orphaned registry entries is to use Piriform's CCleaner]
>Also remove Pando Media Booster.
Update your anti-virus and anti-spybot programs and do a search for any malicious files.
Update any and all drivers that you find; especially for your graphics card.
Attempt to re-install.
You can also try running the program in Compatibility Mode (Windows XP SP2).
If you really want to go the whole nine yards, a defragging of your hard drive probably couldn't hurt either, but thats completely optional and won't solve any bugs.