I thought of another possibility: "Ethernet Addressing". Some ISPs tie their DSL Modems directly to the Ethernet address of the single computer that is first used with them. It's possible (though not commonplace and not very nice) to restrict IP address to JUST that Ethernet address. Some ISPs have been known to do that, but it's controversial, and, understandably, users HATE it. If that's what is happening, you can probably tell your new wireless router to "emulate" the Ethernet address of the laptop that has been working all along. It will then deceive the ISP into thinking that that laptop is still connected.
Regards,
-Peabody-