Are you really connecting it to your PC or to your modem / router?
To change the IP address of the 360, go to the dashboard, go to the System tab, choose Network Settings, then Edit Settings, then Basic Settings. Edit the basic settings and set the IP to manual, if it's not already. Change the IP, but only the last set of numbers. If the IP address is192.168.1.35, change the 35 to anything from 1 to 255 (I think you can use 0 as well, but I'm not sure). As you've already found out, it'll need to be different to any other device on your network including routers, ADSL modem, laptops etc, etc....
If you need more info, post back in this thread. I set up my 360 at home, but I had quite a lot of difficulty getting it to work 100% (mainly with Halo2 and all to do with NAT errors). Good luck!