Hello,Nice forum yall have here.
And now, you're a part, so it's a forum WE have here.
Welcome Aboard!
In your 780, the failed emitter resistor is likely due to a failed power pack (hybrid output module). It could be due to other factors as well. It seems that most often the power outputs in these fail from shorted speaker leads or speaker voice coils/crossovers. They can also fail from overheating due to poor heat conduction to the sink, improper bias voltage/open bias networks allowing runaway, incorrect bus voltages, and probably numerous other potential problems.
What else should I be looking for?
It would be good to test both pairs (all four) of the 0.22Ω emitter resistors. It would also be good to desolder and lift the connection pins for both output modules for testing both the resistors and the modules themselves. Chances are that one of the modules will need replacement, and the other can benefit from a fresh layer of heat sink paste (silicone grease, non-conductive).
With the modules removed it may be safe to power the unit on and check a few voltages. This is safest to do with a current limiting device like a dim bulb tester (DBT) but can be done at normal line voltage so long as the proper fuses are in place. Building a DBT is inexpensive and easy, and provides cheap/effective insurance. Your can find several examples by searching this site.
If all is O.K. the unit should power up normally and should close the protection relay after about a 3-6 second delay. If that happens without blowing fuses or overheating, it would be good to measure the voltages of the DC power supplies. Between the leads of the two main filter capacitors should be +40V on one side and -40V on the opposite capacitor (meter negative referenced to chassis ground). The other places to test are the three larger transistors near the left end of the chassis (viewed from the top), Q25, Q19, and Q20. These three have a "U' shaped aluminum heat sink attached to their collector tabs. You can measure DC voltage directly from the collector tabs.
The rear transistor (Q25) should have about 25V, the middle one (Q19) should have about 50V, and the front one (Q20) should have about -50V. If all those are present and the relay clicks, you may only need to replace the failed output module(s).
Should I just replace the pair while i'm at it?
While maybe not necessary, it's not a bad idea, and it would be good to keep the working original as a spare/backup.
Where can I find replacements?
The original Sanyo output modules are no longer available from the manufacturer. There are several places offering replacements. I've used modules from B&D Enterprises, Electronix, and Consolidated with success. Some are good quality, some are poor quality. A little research might be helpful before ordering.