You need to spoof the MAC address for the modem to the one of the PC you registered with.
On the PC the modem works fine on, go to Start -> Run, then type cmd (then enter or ok)
type 'ipconfig /all'
Depending on how many network connections you have there may be more than one interface, however the one you're after is the one that you connected to the modem when it works. It should be the one with an IP address starting with an 8 if you have the modem plugged in. The MAC address will be in the format of 12 hex numbers (0-F) seperated by -, for example: 12-B5-A4-56-F1-D5. Write this number down, then look for a 'WAN MAC Spoofing' option on the router. If you find one, turn it on, then put in that number.
Save that setting, plug the modem in to the router, then reboot the router.