Broadband router help?

Help? I just got cable broadband. www.warpdriveonline.com Only one available in my area. However, to make this cost effective, I need to be able to put more than one computer on it. Ok, so I need a router, right? I am going to order a router, and need a couple of cards for the puters I want to hook up. But, I called the broadband company today, because I wanted to be able to switch from laptop to desktop and back again, until I get the router. They said I couldn't because the cable modem was configured for my laptop. I can reconfigure for the desktop, but wouldn't be able to go back to the laptop.

Does this make sense? I used to carry the laptop to and from work every day and use it on the network there, and come home and use it on dial up here. Are they saying I have to network my home computers? I thought with a router I wouldn't have to do a network.

I'm confused. Which is becoming the norm!