Yeah, title says it all. I can't even get to an intro movie, which is depressing.
Any help is appreciated, I'd hate to not be able to play this bad boy!
Specs:
Windows Vista Service pack 2
Intel(R) Graphics Media Accelerator Driver for Mobile
Intel Pentium Dual Core Processor
Cheers in advance,
Stygium
P.S. Fool that I am, I didn't actually say the game, did I? UFO Aftershock, downloaded yesterday. Ta!

I have EXACTLY the same problem myself. I hope there's an answer to this one; buying games that I can't play without getting a new computer is very, VERY irritating.
I had no real problems with Aftermath, and my graphics card can still run MOST things, and it is DirectX 10 compatible, so I suppose I don't really understand why Aftershock won't work.

so i guess i wasted $10...again....

Only Aftermath runs on an Intel graphics chip set. The two sequels only run on GeForce or Ati chip sets. GoG has been a bit late in mentioning this as it wasn't mentioned for either sequel until after support got questions about it.

Running the game via wine and linux should work. At least DedZedNub says so on steam:

Basically he says UFO has some strange pixel formats our recent drivers can't understand and therefore can't display.
So, a kind of interpreter would be needed, but so far, hasn't been coded (for Windows) yet.

I had a similar error, related to OpenGl, where the game crashed in tactical mode when loading certain maps (I got an AMD Radeon X1270, however).
The workaround is (a bit complicated,) to run the game via wine on linux. THEY have the correct drivers or wrappers or interpreters, and the game runs just fine!

How I did it:
1. got ubuntu live iso
2. made a live usb (=bootable) via linux live usb
3. installed wine1.6 on that usb
4. ran UFO.exe from out of my Windows installation.

voilà!