Tonight I set out to rectify that.
First up, plug speaker into an audio source and jiggle the cable to see if it's the connector or the cable. Worked beautifully, meaning it's the actual jack on the amp.
Fine. Figure out how to disassemble the thing and pull it apart. (And it it was made to come apart, mirabile visu!) Check jack for bad solder joints; no go, it's solid as the Rock of Gibraltar. Closer inspection revealed the issue: while the shield (outside) of the RCA connector made solid contact with the jack, the pin (center) was not, because somehow the center of the jack had gotten bent out of shape.
Replace it? I went downstairs to see if there was anything in my old electronics kit from school, or in my junk box, that would do; but there wasn't, not even something I could cannibalize. Well, I reasoned, I have to go to Dad's house tomorrow, and that's a hop, skip, and jump from Fry's; but then I reasoned that if I could just bend the pin socket back towards the center, it would work fine. Just needed to remove the heat sink from the amplifier IC, so I did that, and used a dental pick to move metal around. Tested fine, reassembled fine, now it's all spiffy again. Total cost: about half an hour's time, no parts needed.
That is cool. And so much better than the set of speakers I had that came with [PRIOR COMPUTER NAME], which died and were not at all repairable.
I don't make a habit of keeping computer speakers, but I have three pairs which are worth keeping. The set that I use on the desk downstairs, which I bought in 1994-ish; the VOLCANO! set I just fixed, and the digital Boston Acoustics set which goes with Jurai, the P3-1000 I bought in 2001. That computer has a sound card with a digital output, and when I tried setting it up for analog output it sounded terrible--a lot of noise--so I just went back to the digital speakers.
Speaking of which, it probably wouldn't hurt to set up that stuff again and see if it still works....