PS issues can be a common problem. Either shorted tantalums or shorted or open filter caps. An ESR meter might be a good investment.
At a certain point in time when test equipment started to incorporate microprocessors a means of identifying problems called signature analysis was developed. It is relatively simple, but I'll let you find the theoretical papers and read them. In short, you put the instrument into a special test mode, hook up a signature analyzer to the specified points and then use a probe, also connected to the signature analyzer to probe various points. The signature analyzer calculates a value (a signature) and displays it and you compare that with the value for that IC and pin in the service manual. When you find something that doesn't match, you've identified the problematic component without having to track through the schematic and understand exactly what the part is supposed to be doing. Theoretically, of course. Sometimes it gets a little more involved, but you generally get into the problem area.
HP made several signature analyzers, I have a 5004a and a 5005b. The Sony/Tektronix 308 data analyzer will also compute the same signatures (if you get one of those, make sure you get the pods with it). Signature analyzers can generally be found pretty cheap since they're completely useless for anything else. I got my 5005b for $12 out of a buck a pound box at a hamfest. I paid $20 for the 5004a in nonworking shape, but it only needed a filter cap. The 308 tends to be a bit more expensive since it's an 8 bit logic analyzer too which is useful for small projects.