*Have* to use a router.
Is this out of the question because you want to use your existing PCI modem?
If so, you will need to set up an ad-hoc network.
I take it the desktop isn't wireless enabled yet?
If not, you'll need to get a wireless PCI card (assuming you have a spare slot) nuless you can free up a USB port?
That's it really. An adhoc network is one where your computers talk to each other directly with no router/bridge in the middle.
This solution will reqre the desktop to be switched on for the laptop to access the net though, (you'll need ICS on on the desktop).