OK - Windows is updated and there are no problems other than this game.
Just re-reading. You said you deleted the game folder. Did you first uninstall the game via
Programs and Features and then delete the game folder (sometimes there is a folder left after uninstalling) ?
If you deleted the game folder without uninstalling the game then that is where your problem is.
Always uninstall software.
If you deleted the game then there would likely be old registry entries for the game that are causing a conflict.
But where are you with the game now ? Still installed. ? Making a new shortcut from the
.exe in the games install folder still does not help ?
Is your version of the game on disc or is it a download from Steam or other download site ?
If none of the above it may help to run a registry cleaner to see if there are any La Noire entries you can delete (always back up the registry before playing with it ) .
After cleaning up old La Noire registry entries you may be more successful reinstalling the game.
Failing this, try uninstalling the Steam client and reinstall it. Then reinstall the game.
Reinstalling Windows is an extreme measure, and should not be necessary if everything other than this game is running properly.
The options for reinstalling are - reinstalling Windows clean (reformat the HDD), or a 'repair' reinstall (instructions in link below).
Repair Install - Windows 7 Forums
.