If I'm understanding right, that should be possible by setting the wireless router as an access point instead of a router. I can't say anything in the way of specifics, but maybe another member with more experience with this can.

EDIT*************

HOLD UP! If you move the WRT54G into the room with the computer, how are you going to broadcast the wireless signal from the modem/router? Is the linksys wirless also?

If so, the easiest way to do it, would be to buy a wireless card for the desktop. You can buy USB cards, or PCI cards.