I'm afraid that won't work. Does the modem manual say anything about it? Some modems are - in fact - modem/router combinations, and then it might work.
You must have had back luck with your router. It's fully routine, nowadays. So many people have them. With a good setup it hardly can go wrong.
I previously had them through a router but it's been nothing but trouble. Anyways, I have a cable modem which is able to be connected to the computer by ethernet or USB. So could I use both connections on the modem and plug the ethernet into one computer and the USB into the other computer? I hope so but am guessing not just b/c it seems so simple and nothing ever is simple!