I bought a Gateway and then rebuilt it. I bought it 1 year ago and it had a Quad core, 3 GB of RAM, and a 500 GB HDD. Excellent deal at $1000.
You can definitely buy a pre-built computer for your price and even lower. However, Crysis is one of those games that even the best and most expensive computers cannot run well on max settings. Although most people on here will tell you to build it, which isn't a bad idea, but it is not everyone's cup of tea.
You can search through Gateway, Dell, iBuypower, Cyberpower, and that's only naming a few.