Firstly, I would go out and get a can of compressed air (maybe even 2) to clean the board and the rest of the inside of the amp. Given the amp is so old, it probably has stacks of dust on it and a simple clean will help any future problems from happening.
A lot of times you will get just a faulty on/off switch (caused by crap build quality, dust and dirt or wear and tear). You probably have the latter 2 issues. After you have blown out your amplifier I would suggest getting some 'contact spray' - for cleaning electrical contacts. spray the on/off switch and try to turn on the amplifier. If it doesn't work it may be too worn.
Something else that may have happened is that the 'Integrated Circuits' (IC) may have overheated and blown. IC's are the long rectangular black things that have lots of metal 'legs' coming from the side of them- they kinda resemble a bug like a centipede). These little guys are a key component in the amplification of the sound in your amplifier - and they generate quite a bit of heat. When blankets of dust cover one of these or the heatsink that is usually near one, it will get too hot and will short out and cease to work. You can usually replace these easily - just match the number on the IC and stick a new one in the solderless bed they usually sit in.
I think, if your amp powers up - you power supply is still good and that is half the battle won already.
don't work with the amp plugged into an electrical socket and minimize the touching of components - static electrical build up that is released by you touching a conductive surface may damage the smaller components on the circuit board.
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