Have you applied the following patches:
http://www.eyesonff.com/ff7/files/riva_TNT.exe (Only needed if you use a nVidia Card)
and
http://www.eyesonff.com/ff7/files/FFVIIXP.zip

Once you've applied those do as D33p Darkn3ss said:
Just a suggestion. Try right-clicking on the program EXE Properties, and go to the compatibility tab. Then check 'run in compatility' and choose Windows XP from the droplist. See if that works .