You have an ohms test on your Voltmeter?
You can put one probe on the cap where your burn is and trace out the line that connects to that cap and follow it to a point on the other side of the burn. If you read zero ohms you're good, if not it's bad. But you can jumper over that burn with a small piece of wire by soldering to the solder on the cap and just take it out past the burn.
Now, the power supply has about 2 or 3 wire assemblys that go to the left board, called the balancer. You should see by the power connector on the power board 3 different voltages that you must have...5Volts, 13 Volts and of course the inverter output on the plastic-sheathed cable.
You can't check the inverter, the voltage is about 1000 volts, but you can check the 5 and 13 volts....if the power supply turns on properly, you wll see those voltages, if not then you know the power supply is not starting up.
To check for the POWER ON command from the micro, there are 2 cables going to the board on the right side, and you should find a P_On pin clearly marked on one of the 2 cables. Measure it, ON should be 5 volts, and OFF is 0 volts.
That should cause the relay to click on then.
And then the voltages for the balancer board should come alive. ( 5 and 13 Volts).
If you have any more questions just ask, and if you feel your question has been answered, please press the ACCEPT button.