Not going to beat around the bush, that Intel graphics chip is garbage and only good for playing solitaire (if you're lucky). Even if you did manage to somehow get that game to run on that chip, it would be such a slideshow (5-10 FPS if you're really lucky) that it would be totally unplayable.
Unfortunately if you want to play any of today's games (and a lot from the last couple of years) you have a few options,
1. Get a laptop (assuming that is what you have based on the specs you listed) that has a real video card in it (ATI or Nvidia), and even then the low end versions of those will have problems with a game like Bioshock, but at least they will play it.
2. Get a suitably equipped desktop to game on.