What I do is when I'm playing, I open the Task Manager (Ctrl + Alt + Del). Then I look for VC's process. It's called gta-vc.exe (under the processes tab). If you can't find it, go to the Applications tab, right click Vice City, and click Go To Process. On the process, right click it and click Set Affinity By default, all processors are checked.
If you don't want to use Steam in-game, I'm pretty sure that just Alt+Tab to desktop or another program then switching back works. Mouse fix for GTA Vice City, if you are having issues with mouse please refer to this guide. Press many times "esc". After you vack to game (from menu) try to move :)
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