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.
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