When I try to run the game either from the desktop shortcut or from GOG directly the screen goes black, like the game is going to start, then I get an error stating Vampire.exe has crashed.

Does anybody have any advice for running this game on Win7 x64?

I have compatibility mode set for WinXP SP2
Disable Visual Themes
Disable desktop composition
Run as Admin

My specs

i7 4790k
Titan XP
16 GB RAM

Try to change monitor resolution to 800x600 and launch the game. If it doesn't help install the unofficial 1.2 patch: https://www.fileplanet.com/111533/110000/fileinfo/Unofficial-Vampire-Redemption-Patch-1.2 .