Even if you don't see an obviously bad cap, it can still be bad.
You'd need a schematic which may not be available or expensive. Then you need the time to make a project out of it with the right equipment to troubleshoot. You need at least a Fluke or other good multimeter, "GOOD" oscilloscope, etc.
If you take it to be repaired, not many shops doing that anymore. You might have to 'ship' it in. Expensive shipping rates, expensive hourly rates, and expensive replacement parts with markup may make this more expensive than a new receiver. Then you have an obsolete old receiver.
Probably just time to upgrade. It might be more cost efficient in the long run.
I just bought the Onkyo TX-NR6050 for $400 from Costco. It's a Costco exclusive receiver on sale right now. It's pretty much a $800 TX-NR6100 without the THX surruond modes and Relative volume display. Or closer to a $900 Pioneer Elite (another Onkyo made receiver) VSX-LX105 without the RS232/Zone 2 IR/Triggers.