I don't get this error...

Intel's chipsets are legendarily bad, I've used the precursor to the one you're using (it's in my mom's old Dell). It definitely won't run H2V at anything playable. I tried running H2V on my laptop (integrated GeForce 6150SE) and it was almost unplayable at minimum resolution (game supports a minimum of 800x600 if I remember correctly) and low graphics settings. The GeForce 6150 had a lot more power than intel chipsets did at that time, at least from my experience.

The 7300GT requires a 350W power supply? I wouldn't have thought a low-end 7-series would require even 300. Though the only thing I'm going on is that my 9500GT requires a 350W, but I'm guessing that it's a bit more efficient? Certainly is a more powerful card.

Well I was planning on getting a lap top this summer so I'll make sure I get a good gfx card non integrated.

Most laptops that are reasonably priced have shit graphics cards available to them; get a desktop.

As this topic isn't locked yet, I'd like to address the main issue: You undoubtedly lack Hardware Transform and Lighting support on that Intel card. Of note, it doesn't do Vertex Shaders (it is emulated, though, hence why you see Vertex Shader: 2). The graphics engine in H2V requires T&L to function - it doesn't even have a Fixed-Function fallback. Personally, I think this was a ballsy move and a horrible choice on the part of the devs.

Intel graphics suck, Nvidia (or ATI) all the way. Don't even try to game with an Intel card.