Laptop Schematic

Networking a laptop and a desktop to one printer?

I just recently purchased a HP laptop with Windows Vista. I have a desktop computer with Windows Xp that is connected to cable internet through a Linksys router (with a ethernet cable, in other words wired). The desktop computer is also wired DIRECTLY to a HP printer Deskjet 3940 printer. I have several questions. I know I can easily connect the laptop to the internet wirelessly but would I be able to share the printer with the laptop if the printer is directly connected to the desktop computer? Is there someway that I can share the printer through the desktop pc, through the router (which is being used for internet) to the laptop (without the pc being on)?
I made a really simple “schematic” of the setup on Paint:

http://img136.imageshack.us/img136/9500/networkschematicov5.png

You need to share your printer. In the desktop computer go to Printers, right click the printer and click Shareing. You need to create a network for both computers. Go to Control Panel, Network Center.

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