Agree with davidgo. Now, if your modem is a pure modem (or a router in bridge mode), you can try spoofing the MAC address of your router as that may be what your ISP is looking at.
Does the router have a configuration that includes a username/password or keypair information? If so, the ISP may have client software for the PC, or a Web Page for entering this data.
Also try a crossover cable. The router may have auto-MDIX.