I hope BobbyRaw's advice works. It's worth a try.
A thought has occurred to me. You mentioned that you still log on via your old modem desktop login. I spot a problem there, in which case Bobbyraw's advice has merit.

With PPPoE set in your router, you should simply sitch on your connected (to the modem) router and it will negotiate the ISP logon. Then fire up IE and if your settings there are correct (Obtain DHCP address automatically), then on either computer you should get through. Gorget about the log on from the desktop icon. That's how it should work.

Something makes me nervous about the 5260. It's apparently hackable, but not user configurable otherwise. If it's aold, then the firmware is old and it simply may not serve dynamic IP addresses; it would explain why it works on one link when you log on from the icon and thus why the second PC won't work.