I'm with nctnico; start by checking the rectification diodes and then move onto the regulator.
However, while powering up the negative regulators from a bench supply is a good idea, I don't think it'll work here. I've attached what I think I'm seeing, and rather than using 7905s and 7915s for the -5 and -15 volts they seem to be zener referenced off the +15v supply (which I presume is working). So they won't work unless the +15v supply is also up and running.
Can you safely access the back side of the supply while it's hooked up, keeping in mind that there are lethal voltages on the high voltage side?
This is what I think I'm seeing. This is only one channel but the other looks identical:
(EDIT: Oops, the polarized capacitors are upside-down. Force of habit.)