Because I cannot "add a new printer" on the laptop (no printers are
found) I don't know how to check and see if print sharing is enabled on the
new laptop. Isn't that under "properties" of a printer? I don't have a
printer connection.
No, it's not under properties of a printer. It's under properties for the
network connection. In XP, file and printer sharing is off by default. Once
that's enabled, the laptop should at least be able to sense the presence of
the networked printer
Have the printer powered up and connected just as you did with the previous
laptop. At that point, you should be able to "add" the printer or at least
"map" to it. Next, XP should tell you whether or not it needs the printer
drivers installed as well.
Someone else mentioned firewall - definitely worth checking out on the
network and on the laptop.