There were no fuses under the control panel, but I traced the coil wires — one wire from each coil goes to a box next to the PSU that contains a single common T5A fuse. This fuse was fine. In the same box there's also a rectifier bridge, which I tested with the diode function and it seemed OK, and one 10,000 µF / 50 V capacitor, which measured 12,000 µF on the meter. So it looks like the fault must be somewhere on the PCB.
I also measured the 74LS32N chip on the PCB using the ohm range. All inputs to ground showed roughly the same value, and two outputs to ground showed roughly the same (if I remember correctly, about 400 kΩ), but the other two outputs to ground were only about 0.9 kΩ. I don't know if this is normal or not, or what else I could check.