Can't access printer on home network

I have a desktop and laptop connected on a wireless network. The desktop is
running XP Pro and the laptop XP Home.

I am the system administrator on both machines with family members having
(limited) user accounts.

A printer is connected to the desktop with all users having printing access.

From the laptop I was able to use the Add Printer Wizard to connect to, and
network access, the printer connected to the desktop. For some unaccountable
reason, that access has now disappeared. Clicking on properties from the
Administrator (laptop) acccount I get the message that I do not have access
and only the security tab will be displayed. Trying the Add Printer Wizard
again, I'm able to navigate as far as "Desktop" but double clicking on that
doesn't bring up the printer. I get the same thing when trying to add the
printer through the other limited user accounts. Neither can I connect by
manually entering the desktop destination of the printer.

Previously when the printer was working from the laptop Administrator's
account, and going into Printer Properties clicking "Share this Printer" the
sharing symbol would not display with the printer icon. I clicked off sharing
and re-booted and repeated the sharing process but to no avail.

I suspect this may have something to do with the settings in Printer
Properties under the sharing and / or security tab accessed from the Desktop,
but I can't find the answer. From here I've given permissions to "Everyone"
but that makes no difference.

I'm really quite lost on how to get around this problem. Can anyone suggest
any solutions, please ?