"Sharing the Internet" is more than providing a wired link between two computers. You're going to need to configure the network stacks of the two computers to utilize the wired link properly.
Assuming you're using Windows XP or newer, use Google to find out more about the "Internet Connection Sharing" feature. It should take care of most of the configuration for you.
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What kind of system are you using?
Mac or Windows? (Linux?)
I'm not sure if you can do it with a crossover cable, but I do know you can do it with Ethernet or Firewire on a Mac.