I KNOW what I am doing and talking about...
Are you sure? I'm not so sure. Anyone have any opinions?
jplainview - You asked a fair and straight question, and got a straight answer. Mark eats, sleeps, breathes, and dreams Pioneer. For some reason unknown to many of us he seems to have an affliction with the brand, specifically, but his broad background gives him a a solid base for diagnosing this kind of thing via keyboard and monitor regardless of the name on the front panel. You're lucky he takes the time to look at all these threads and share his accumulated knowledge. We're all lucky that he spends so much of his limited free time here.
We're also very fortunate to have other highly skilled and experienced resources, and you've been lucky enough to have several of those also chime in. Like MTF, Dr. Audio, Pete, and Zeb1 will not steer you wrong. The rest of us will tag along with the thread and help out with the common and easier things, but when the real head-scratching begins, those are the resources you want helping out. There are others, but you have already met some of the best.
As for the meter, your model should be adequate for the diagnosis and setup of the unit once (not "if") it is repaired. The hFE (gain) measurement feature might also com in handy if this process goes a little deeper.
Regarding the stereo, the 790 is a keeper. There are LOTS of 780s still out and around, still singing along. There are a lot fewer 790s. While they are functionally identical, the 790, being more rare, is somewhat more valuable.
If you haven't already done so, visit the AK database or other resources on the WWW and download the service manual. One thing you may find is that the diagrams in most of the scanned service manuals available for download are unclear, cropped, or sectioned in such a way that they may be difficult to read. Having had five of these units I got so tired of fighting it I reconstructed a clear copy. You can download the cleaned up copy HERE:
http://www.wwdsltd.com/files/SX-780Schematic-Wide.jpg
There is also a cleaned and complete version of the board artwork for download HERE:
http://www.wwdsltd.com/files/SX-780PCBoardLayout.jpg
Hopefully that will make it easier to follow the manual and AK suggestions.
A pencil-type solder iron of 30-40W should be sufficient for most of what will be needed here. Anything larger can be dangerous due to the potential for excessive heat. It isn't critical to get anything more than a rudimentary iron, some solder paste, a bit of 60/40 solder (preferably flux-cored), and possibly a desolder bulb and/or solder wick to help cleanly remove old components. There's no benefit to a grounded-tip iron in these devices, although it wouldn't be a real problem if that's all you could find. If you haven't been there before, practice a bit on scrap wire, boards, and components. Desoldering and resoldering on old, discarded devices is a cheap way to develop good habits.
The rest should be basic hand tools, your time, and a willingness to succeed.
That should be a pleasant unit once it is returned to service - Well worth your time and attention.