Obviously, i'm dumber than a box of rocks, or Microsoft has crappy stuff. (hmm.. which is it? or can I choose both!?)

Currently: Have a LAN running Win NT4.0. We are moving to a new Server2003. I have assigned a different domain name to the new server.
Now, yesterday I did a 'search for computers' on the new server, looking for the old one (by ip addr.). found it, and was able to move some shared documents, etc. over.

Today, I cannot 'find' any of the computers on the NT4.0 LAN.

Have rebooted both servers, both are connected to our ISP. What am i doing/not doing correctly?

I am under the assumption that both domains are on the same subnet. You could just setup the two WINS servers to replicate with one another in each domain to speed up resolution, but I would just use \\machinename\share to get what I need.