I run Messiah on Windows 7 Pro 64bit with a Geforce GTX 560Ti and latest drivers. I'm using CoffeeJones solution to the graphics problem:
I found a thing on the forums that HELPED ME GET THE GAME TO WORK!
"Run the game with the -x flag
That is: C:\Program Files (x86)\GOG.com\Messiah\MessiahD3D.exe -x
... and you'll see a dialog box with a choice of resolutions.
Then you'll see a screen like what's attached below.
Switch device to Direct 3D HAL not Direct 3D T&L HAL.
You should be OK to play the game.
Another solution is the use of a Glide Wrapper.
Use Zeckensacks Glide Wrapper (http://www.zeckensack.de/glide
/) and install it (a restart is maybe neccessary).
Get the 1.2 patch from here: http://dlh.net/cgi-bin/patdl.cgi?lang=ger&sys=pc&file=mess1_2.zip&ref
= (or from elsewhere)
Unzip it and copy the Messiahglide3x.exe into your Messiah directory
Create a shortcut and set compatibility to Windows 98, disable "visual themes", "desktop composition" and "display scaling..."; enable "Run this program as an administrator"
After starting the game with the shortcut you're asked for CD2 of the game.
DON'T PANIC! Click it away three times and the game starts nonetheless. "
Hope it helped, it did for me!