Electrolytic capacitors in the power supply are a good place to start with anything a few decades old. They have a limited lifetime no matter the quality of the capacitor. As they go bad they lead towards all sorts of problems so it’s usually best to get those out of there then do more diagnosis from there.
You can also measure power supply voltages with a voltmeter/multimeter and see if they are as they should be. It’s usually good to take some measurements before going and replacing stuff.