I'm sitting in front of an XP computer right now so maybe I can clarify things a little. Starting from the beginning to avoid confusion:
First write down the share name of the printer on your desktop. Then write down the name of your windows xp desktop; in your case I think you mentioned it was your last name.
Then go to the laptop and click
Start --> Printers and Faxes (or if you're running the classic start menu click Start --> Settings --> Printers and Faxes)
Once the Printers and Faxes windows is open select Add a Printer on the left
At the first screen select Next
Select: A network printer, or a printer attached to another computer
Click Next
Select the second option box "Connect to this printer"
In the blank field type two backward slashes, your computer name, one backward slash, and then your printer share name
e.g. \\yourcomputername\yourprintersharename
I can't go past this part on my own because I don't have a printer to connect to with the computer I'm at now. You should just be able to click next then finish or something
If it doesn't detect the printer make sure the names are correct and that the printer is shared on your desktop. Also that you don't have any firewalls like Norton or McAffee installed and running.