Actually, the problem is more insidious than that.

When I'm on .3.x and the player is on .4.x, even if I spec the player's IP address directly in the Emplode connection screen, it does not connect.

When we're both on the same subnet (.3 or .4), the network broadcast still doesn't work. But at least if I spec the IP address directly they work.

This is actually all a bit academic, as I'm sure if I asked our network guy if he could give me a couple of static reservations, he would. He's just in the office next to my cube. Doing this would solve my immediate problem, but I'm also interested in the general case, what causes it, and how one would work around it.