^ Pop the console open and look around. Given its age, I'd look at the capacitors first, but of course any burn market, cracks in the PCB or solder joints, and then whip out a multimeter and probe around. Just as a sanity check I'd try a different game cart first.
Sometimes I'll pop open PSU just to see what went wrong. Back then they were probably unregulated and it's the thermal fuse in the transformer, or a power surge took out a diode(s). However some of the modern replacements may be low quality switching PSU, especially if a generic brand.
More recent PSU are usually switchmode with the failure being a burst output filter capacitor. Sometimes it's like clockwork to get about 5 years 24/7 service before failure. Being sealed they run hot and use mediocre quality caps. I'll put a top shelf cap(s) in, and drill some vent holes in the casing. I don't have little kids running around that might stick metal objects in anything with a hole so it's not a problem putting the holes in.
I expect the repaired PSUs to last longer than a new one would, at a fraction of the cost, and minimal downtime because I have stock of popular cap sizes that fit things like wall wart PSU, monitors, computer PSU, etc. Granted if it's a popular PSU form factor like 12V/1A and 5.5mm barrel connector, I have spares to use then when the failed one is repaired it's put into the spares pile.