Networked printers often do not show up on the network in the way that
computers do but they are there none the less.
This is often because the printer's network address is determined by the
printer's networking device rather than assigned by the router.
I suspect your HP device is a wireless USB print server and not a network
print server but I am guessing. If it is indeed a wireless USB server the
laptop will not be able to connect anyway unless the desktop is turned on.
If you have the desktop connected to the printer via a USB cable and it is
working properly then it should be shareable, but you are using Vista which
has the worst networking of any Microsoft OS ever. Win7 does not seem quite
so bad.
If you have right clicked on the printer properties through your desktop and
enabled sharing for the printer you should be able to connect to it with
your laptop if the laptop can see the desktop on the network. Make sure that
the desktop is setup to allow sharing of files and printers, which is
usually turned off by default. I suspect this is your problem.
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