Actually, you're wrong about the DHCP server for a cable ISP.
Remember, the cable modem is on the WAN side of the router, and almost all cable ISP's do indeed have DHCP capability and the router is normally set for WAN dynamic addressing. On the LAN side of the router, most home networks also run the DHCP server. I normally let it have 100 addresses, and then assign any static IP addresses in the unused area of the subnet.
With a plain cable modem, resetting that router to factory defaults should result in a good wired connection. For that router, you'll also have a wireless connection, though it'll have no encryption.