Splitting internet connection between 2 PCs?

Hey all, was wondering if I could possibly get some advice with regards to this:

Basically, last year I had a cable internet connection. We had a router, and it was split between 4 computers and it worked fine.

I've recently moved to a new place, and cable internet isn't available for whateve reason (the place is slap bang in the city centre, so lord knows why I can't get it.)

Anyway, excuse my lack of the proper terms, but I've managed to get broadband with a company called Tiscali that goes through the phone line (ADSL is it?).

The connection goes through the phone line, to the modem (through one of the standard wires that you use for dialup) to the modem, and then the modem is linked to my PC via a USB connection.

Internet works fine, but my flatmate gets back in a couple of weeks and since the router we had before is no longer going to work, I was wondering if anyone knew how I would be able to split the internet between the two computers.

Would I need to buy a new kind of router, or someone mentioned using my computer as a router, but I have no idea how to do that.

I'd be very grateful if anyone could give me some advice, and congratulations if you've even made it to the bottom of this post without falling asleep.

Thanks!

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