When I open up the system, there are no obvious culprits. Everything seems clean and in good shape. I believe that the tray belt was replaced at some point because it is in great condition, and I believe the C2103 was also replaced at some point because the soldering looks done by hand.
As mentioned, it plays a CD for a few minutes and then stops. Sometimes, if I try to open the tray right after it stops, it has trouble doing so, as if the tray motor is not getting enough power. The problem seems to get worse the more I fiddle with it (yikes). Interestingly, it works fine when the decoder board is upright in "service mode". It's only when the board is down in its normal orientation that the problem manifests.
I'm a novice with electronics, though I have some soldering experience. I ordered replacement caps from BeoParts and started with a big one (C13) that looked like it might be a little worn. But it's a 4-pin cap, and the replacement is a 2-pin cap. When only 2 pins are soldered in, the machine is totally unresponsive, so I put the 4-pin cap back in until I can figure out how to turn a 2-pin cap into a 4-pin cap.
I'd be very grateful for any suggestions for how to investigate this, or if you're in the California bay area, I'd happily work out an arrangement for some in-person help.