You don't even need a router but it is better with one, you could just patch the two together with a cable vie network cards, the only problem is that you will need the computer with the incoming broadband connection switched on to enable the other to have a connection but it works fine.
look on the back of your broadband modem
near where the cord from the phoneline connects .... are there any more sockets?
if not - it sounds like you are using a USB modem ....
ratters is the cheapest option and only requires a crossover cable (�3.00 or so) - assuming both PCs have network cards ...
.... see help or google "internet connection sharing" (ics)
Ethel's suggestion is more costly �50.00 ish
but gives the greater flexibility.