Like they said, you should get a router. I've had cablemodem ever since it was new, I used to live in West Seattle, and we were one of the first test areas to get it. You used to be able to use a switch with no problems for quite a long time. But the last couple years I think they changed some things, and you may have a much harder time than the old days.
Your cablemodem will only receive one IP address. A router can take one IP and turn it into many IP's. A switch doesn't work that way, it's only a dumb switch. Your computers are conflicting with each other, both trying to use that one IP probably. You will probably have a hard time getting both computers to use the net simultaneously with that thing. It will work with one computer. Then you'll probably have to cycle power to the cablemodem, before you'll get the other to work. Only ONE will probably work at a time. The other option is, I believe you can pay a little monthly, for an extra IP address, then your switch would work. But I wouldn't do that, waste of money, a router will pay for itself in that case.
Personally, I'd quit screwing with it, and go with the answer you've been given multiple times, you need a router. Otherwise you're asking for alot of headache.
edit-- lol whoops didn't notice this was a week old, dude probably sorted it and bought a router
I'm not a complete idiot, some parts are missing.