Check # 31 in the bug list with solutions thread (in the first post)--- this is fairly common on newer PCs (windows 7 or later)
If your PC does not support 640 x 480 resolution then the game will hang on startup.
Specifically what occurs-- when the game starts up, it checks for the gta_vc.set file on your PC-- this is the game settings file and will start up in what ever resolution is in that settings file, if that file is not found, then it will create a new one and start up in it's native resolution (640 x 480)-- if your PC does not support that, it will hang on startup.
The above solution is to use one or the other of the settings files I created on my PC to get you past the check.
Please try to use both of those settings file (if the first one does not work)-- and report back if the game starts up.