LuckyRaccoon, my own advice would be: upgrade yours drivers, straight from Intel. If it doesn't work, try playing with the flags Gandalf mentioned. in particular -xxx and --noglext. You might also want to try other 3D games and tell us which ones work, if any (I don't think the problem comes from Dominions as such).
Regarding the Intel Graphics card: the Intel Graphics 950 should have enough firepower to play the game, and its specs are definitely higher than the first Geforce cards. More significantly, Intel claims the 950 can run
these games and Vista's Aero interface, so it should be able to run Dominions with decent performance, at the very least.
For that matter, Dominions doesn't actually require a 3D card in the first place; my old computer could run the game with only software support (Mesa on Linux), though it didn't have much in the way of processing power. It was slow, of course, but it works - if you don't mind its s.l.o.w.n...e..s...s.
As I understand it, the 950 doesn't have support for some advanced features, the like of hardware T&L. Still, I'm pretty sure Dominions doesn't require that kind of feature, since the game runs under software Mesa. But you do need *some* kind of OpenGL support somewhere, so that means proper drivers.