I'm also getting the exact same problem. Crashes to desktop with this error message. When I go back to the game, everything is black.

Very disappointed as I own the original CDs which had tons of problems, so thought GoG would have patched and fixed it now so bought a copy here.

Does GoG do refunds? :(

I have the same problem. It crashes right efter the intro. Tinkering with the options didn't help. It really pisses me off.

Try following the steps in this thread exactly.
Also, if I tell you in there to do something that for some reason doesn't work with the gog version, tell me and I'll see if I can improve it.
Oops, by 'this thread' I meant http://www.gog.com/forum/messiah/messiah_composite_quick_start_thread