Shame you can't use an Amiga PSU. Without powering the board you could do a continuity check on the circuits and see if any of the tracks are faulty. I've had a similar problem with a bent pin to a chip particularly the main processor. Also check for damage to pin seats inside the chip socket. Look for corrosion around the Agnus. Do not pull chips without the special tool. Fully remove the board and have a close look underneath. Check also for dry solder joints at say the power supply etc where excessive plugging in and plugging out can break jounts.
Did the floppy kick in. Sometimes you get a click. Also depressing one of the switch pins may roll the drive round. Get an external drive and check also with that. Make sure all the chips are the right way round. You didn't mention what the power light was doing. Did that flicker on and off.
By the way they build aeroplane flight recorders out of Amiga 500's cus they are impossible to break. My guess is a circuit is busted from usage from one of the back ports. Could even be a ROM. I've had all kinds of problems preventing an A500 from not working. That's why I keep a big box of spares of everything so I can swap stuff out.
Have fun.
