I googled to try and find a solution for your printer and found this is a common problem.  Below is the solution to your printer problem.

Problem fixed: I finally got it working; here's what I did:

1. Renamed the shared printer (from "hp deskjet" to "hpdeskjet") on the desktop - just to make sure spaces weren't causing any problems.
2. On the laptop, I went through the Add a Printer wizard, but selected the local (not network) printer option.
3.(Add a Local Printer, Create a new port, Local Port) When installing locally, I used \\desktopname\hpdeskjet as the location/name (where desktopname is then name of the desktop machine that the printer is connected to).
4. When it asked to select a driver, there were 3 choices, 2 from HP (ending with HPA), and 1 from Microsoft. I picked the Microsoft driver.

That worked for me - just make sure it's the default printer on the user accounts on the laptop.

I got the solution from here.

If you need help finding your computer name on the xp desktop cri posted a good tutorial here.