I get the impression that your desktop was connected to the router via ethernet cable, rather than wireless. Could you access the modem from your wired desktop through the router (via the modem's local IP address, likely 10.0.0.1 or 127.0.0.1)? Alternatively, once you are directly wired to your modem, you can access it directly and then see if it recognizes your router as a connected device. If there is no communication between the two, then you might check the cable connecting the router and modem as well (presuming it wasn't one of the two cables you previously said you checked). If the two can't communicate and you've confirmed the cable good (also, try changing the ports plugged into on both the router and the modem, on the off chance one of them decided to retire early), then you can probably consider the router to be kaput. If you can talk to it, check various configuration settings for the wifi, and also that you don't have both the router and the modem set up as routers - one of them should have DHCP disabled so they don't fight each other, though it is unlikely that this would just pop up randomly long after being set up.
Mike