Cannot browse computers by name over LAN, only by IP

Using XP Pro SP3

I have a Local Area Network in my home. I have systems running XP home, XP
Pro, and Vista. All but one can access the Network Attached Storage device
(NAS), which is a Seagate DockStar. The DockStar is using Windows NT 4.9
Server.

The one system that cannot see the NAS has had problems accessing shares in
the past. I have followed some advice and made some registry changes, and now
it can see other computers on the network by name, but it still cannot access
the NAS by name. Attempts to connect to it by name result in the following
error message.

"NAS name is not accessible. You might not have permission to use this
network resource. Contact the Administrator of this server to find out if you
have access permission. The network path was not found."

Interestingly, I can browse the NAS from this computer by using its IP,
rather than its name.

None of the other computers on the network has this problem connecting to
the NAS. They can all connect to it by name, including another one that has
WXP-Pro SP3.

What gives?

Any assistance would be greatly appreciated.