Capacitors do "dry out" over time and can fail. Since, you're working on a LPIII laserjet of some vintage, its not uncommon to have bad caps and thus fail due to age. Glad you got the printer running again.
As we know, there are two modules which are the most likely to be responsible for "50 SERVICE": The Fuser and the AC Power Suply.
After testing 1,2Mohm and 7,9ohm in the Fuser module, I found the defective component at the AC Power Supply module, it was the capacitor C153 which was leaking a bit and fouling around on some diodes and a transistor.
I have replaced with success the original C153 of 22uF/25V by a tantalum capacitor of 33uF/35V (I haven't any 22uF/35V to hand).
The PCB was cleaned with alcohol, and ones the printer was reassembled, the display did show "READY" instead of the damned "50 SERVICE ERROR"
Possibly, the reason for the leak was an over-voltage and not the typical thermal failure, because there wasn't any hot component in the vicinity.
I hope this could be of interest to keep on working this very classic printer.