Two computers one cable modem

My cable modem only has one cat5 jack, one power jack and one coax jack.

Sooo, I was wondering...is there a way (without doing the router route) to hook up my two computers, using a cat5 switch or hub or wha?

See, the buggy part in this setup is when I switch from my Intel based computer to the AMD based machine.

Sometimes, the AMD thingy just doesnt get the message that it should be connected to the internet and the modem keeps resetting. BUT, other times it runs fine! Sheesh!

So, I think the problem is in the unplugging and plugging of the cat5 cable.

My two computers are essentially a study in redundancy. Each has 6 hard drives...2 with Windows 7, 2 with Ubuntu 1010 and 1104, one with XP pro and one with XP Media Center.

And at least once a week I go through that update hassle, so I need both systems hooked to the Net! You know what I mean?

I have a decent modem. (Motorola SB6120 Surfboard Extreme) and when Finally hooked up to the Internet, I can do anything I want, without hiccups!

So basically, the bottom line is...How can I get two Cat5 cables hooked up to the Modem at the same time, so each machine is always connected...so I dont have to go through the modem resetting boggle, when I switch?  

BTW...This is a legitimate question. Normally, I should be able to be able to figure this out myself. This one has me stumped, though.

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