It seems like your computer is running in the DMZ. Make sure that you don't have any computers configured to be in the DMZ in the router config.
Ensure that your router is configured to be a DHCP server.
Make sure that both computers are set to "Obtain an IP address automatically" in the TCP/IP properties of the Local Area Connection Properties.
Turn off your cable modem, router, and both your computers. First turn the cable modem on and allow it to fully initialize. Then turn your router on and let it fully initialize. After the router is up and running, turn on your roommate's machine first and allow it to load, and then turn your machine on. Once both machines are up, check to see if both have a connection. If they don't, check the IP that both are using. They both should be of the format 192.168.1.* or 192.168.0.* (unless you changed the router's IP address and subnet masking).
As for thinking that the IPs should always be 192.168.1.10*, that's a good idea, but it all depends on how you configure the router. If you change the router's IP address to 10.0.0.1 with a subnet of 255.255.255.0 and tell the DHCP server to start numbering IPs from 50, the first computer to lease an IP from the DHCP server will have an ip of 10.0.0.50. As I said above, make sure that your DHCP settings and DMZ settings are correct.