Basically, it sounds like you're screwed. Uninstall Vice City, then go in and delete any folders that may be left behind. Go into your My Documents folder and rename the Vice City User Files folder to something else (doesn't matter).
Next, reinstall Vice City. Once you have Vice City reinstalled, right-click on VC's install folder and select "Properties". Click the read-only button and then click "Apply". Make sure that the changes you make apply to the folder and all files contained inside. After the pc makes the changes COPY THE ENTIRE VC INSTALL FOLDER TO ANOTHER LOCATION. That way, if your original install becomes corrupted, you have a clean installation to copy over and overwrite.
Once you do that, start up Vice City. If you can play without the game crashing, then go back to the backup Vice City User Files folder and copy in your game saves. If you still can play without the game crashing, then you're good to go.
Hope this helps!