Given that your PC pulls an IP address from the gateway with no trouble, my assumption is that the problem is the Xbox360. DHCP is an incredibly simple protocol and usually when something's not working properly it's a simple problem, and the fault isn't with DHCP.
Make sure it is configured to get its IP address from DHCP. Also, this may sound obvious, but don't forget to double check the cable connections, try plugging the xbox360 into a different port in your router (try the one the PC is using)
Check the range of IP addresses your router can give out, and it's current leases, perhaps it's exhausted. Increase the range if this is the case.
If all else fails, give your xbox a static configuration (copy the ip information off your pc, and just change the IP address) and see if that works. Although that's not likely
Help! I'm stuck in a forum signature!
