Old machines that sat around for ages tend to pop a capacitor after they are on for a short while. One of my mint IIgs systems died after 30 minutes of use after sitting in somebody elses basement for many years. It was cheaper to get a replacement then to fix the old one, but I kept it for when getting a replacement will cost more then fixing the dead one.

If the capacitor burned it was probably a small one, easy to find on the PCB and probably also easy to replace. My old PS has a dead short somewhere but nothing is visible and no smoke came out.