Well, you certainly meet the system requirements of Prison Tycoon 4, and it says it runs on Vista.
First, open the device manager and see if there are any yellow '!' marks next to anything there, just to check that all of your device drivers are installed properly.
(To open the device manager in Vista, either right click on 'Computer' and select 'Properties', or go to Control Panel -> System, then click 'Device Manager')