[ecurbh]

Just thought of a problem, though... if one of us must be connected to the cable modem, how does that person connect to the router at the same time, so that the other computer can access it?

Oh yeah, I think I have an extra USB network adapter around. My computer is currently connected through a built in adapter on the motherboard.

[Bear_in_RoseBear]

Are your computers networked to each other currently? Or were they networked through the non-working router?

If they're not currently connected to each other, then it won't work... but you could get a cross-over cable to direct connect the computers, or a little mini-switch or hub.