Hey Oliver,
thanks for your extended reply. To start off, I didn't try to discharge any of the equipment. I was inspecting it and when I moved one of the capacitors, I saw a discharge, and then noticed the connection was broken. I did test the caps voltage before I worked on them though

Secondly, yes, I'm very careful about the live wires and wearing some protective equipment is recommended.
As for replacing the whole PSU, well yes that's an option, but if I can fix it, I'd rather do that, so I can learn a thing or two. The unexamined live isn't worth living

As for the 2nd power supply, yes, it's a switching power supply, and yes, I noticed the power rating is a bit lower.
Finally, the info on the transformers (rust, whinning/humming when new, etc), was great! I had no idea. Thanks for that in-depth info, it was perfect! If you have any other such tid bits, please tell

If you want to take a stab at this:
How do I determine if the transformer is dying or the whine/hum is normal?
Same for the whole PSU? Maybe it is OK after all. I'd like to learn if there's some easy steps to check the "health" status of said PSU.
Thanks again!