There may be nothing wrong with the ethernet ports in that conduit. The problem with the ethernet may be on the other end of the wire. I would expect each of the ethernet jacks to have its own cat5 wire. All those cat5 wires probably go to the same location in the basement or a closet. Getting the ethernet working may be as simple as connecting the other ends to the internet. You would usually do that by getting a network switch with many ports and plugging all of the cat5 cables into it. Then you would need to connect the switch to your router with another ethernet cable.

Well, this raceway goes around 3 walls of a single room. The adjacent rooms do not have such a raceway. I assumed the purpose of this would be so you can have multiple computers in the room all connected to the same Ethernet circuit, without cat5 cables lying everywhere. But I was surprised to discover the jacks are not connected to each other.

There is a separate ethernet cable coming through a separate hole in the wall, from the other room. I've tested this cable and it is functional. I assume it was supposed to be plugged into one of the raceway's ethernet jacks to link the two rooms together.

There are no devices connected to this from what I could tell, nor any place that looks like it could conceivably house a "hidden" switch.

Hmm, but after thinking a bit more about your comment, I think I can see how not every pair of ports would necessarily be connected. I only tested a few at random, I didn't comprehensively check every pair. I'll try that!