Set vc-mp.exe in it's Compatibility Settings to Run As Administrator and to emulate Windows 98/ME for all users. Then set gta-vc.exe in it's Compatibility Settings to Run As Administrator for all users. Also copy over your VC settings file (gta_vc.set) from Documents\GTA Vice City User Files\ to C:\Users\Public\Public Documents\GTA Vice City User Files\ so that when you run it as an admin, it still reads your settings.
Lastly, test Single-Player and make sure it works beforehand. If you are using a downloaded, illegal copy, we can't support you here. Piracy is illegal.