So the game has downloaded fine, but when I can launch it (either through the Start menu or launching it straight after downloading) nothing happens. Any suggestions on what to do?

If you are using a nvidia card have you downloaded the latest drivers? Its only with some of the more recent drivers that this game will run.

Launching it straight after downloading ? Does that mean the game isn't installed yet ?

If the game isn't installed yet and the installer doesn't seem to launch and if you are on Vista or Win7 it could be that UAC is slowing down the install process. You could either wait a few minutes untill UAC finishes checking the installer or you could temporarily disable UAC to speed up the install process.

But reading your post i'm not sure if the game is installed and doesn't start or if it's the installer that doesn't start.

Try running the .exe as Administrator.