the way i do it, is share the printer on my server, which would be your compaq in your case. the easiest way to share a printer and/or network drive, is to be in the same workgroup.
so on your compaq, right click on My Computer, and go to "Properties", then click the "computer name" tab. then click the "change" button near the bottom. click the "workgroup" radio button, and change it to whatever you want, and make sure that "computer name", top is an original name, for now i am going to call it CompaqDesktop. it should ask you to restart, so restart now.
then do the same on the laptop, making sure they are in the same workgroup, except change the "computer name" box to something other than the compaq's, then restart.
this next part you might have already done, but let's make sure.
on the compaq, go to: Start - Printers and Faxes (or if you have the classic style menu: start - settings - printers and faxes) and there should be an icon called something like "hp photosmart". right click on it, go to "properties", then in the "sharing" tab, make sure the "share this printer" tab is clicked, and make the name something like "HPPhotosmart".
then on the laptop, go into "printers and faxes" and on the left click "add a printer"
in the wizard, check the "network printer" radio button. then Click "next", then click "browse", but instead of nothing found, now it should have a tree list, with a list of computers and printers on your network. if the printer shows up, click it and continue, and set it as your default printer. you are done!
if nothing still shows up, your compaq computer might be hidden or something, but fear not, there might be a way around it.
go back to where you selected to browse the network. and select "connect to this printer" and with the names we selected earlier you would type:
\\CompaqDesktop\HPPhotosmart
then continue the same way through the wizard
hope that helps.
