This cute little receiver from Onkyo, the R-805X:

has a pretty bad design flaw, which leads it to eventually just click the power relay and never boot up. This is due to a couple high power resistors being placed in close proximity to an electrolytic capacitor. Here is the board area that causes the problem:

Notice the browning of the board near the center. Another view from the side of the PCB, the affected capacitor is C919, right next to the plastic pole support sticking out of the board:

Another view from the front of the PCB:

And finally a view from the top of the PCB:

You can see heat damage on the top of the PCB as well. All this heat causes the electrolytic capacitor (47uF/50V) to fail. The fix is simple, just replace the capacitor, and maybe bend the power resistors slightly away from it! I ended up using a 160V capacitor since it's the only thing Fry's had at the time. You can see the replaced cap in the center here:

It is a bit tricky to replace this cap since the main board has to come out. I had to pretty much disassemble the whole radio:

Although in retrospect I don't suggest anyone do the same! It should be enough to:

1. Take off the top cover
2. Remove the 3 remaining screws holding on the back plate to the chassis (do NOT remove any of the screws holding on the connectors, it's not required)
3. There are 3 screws holding on the front panel, 2 underneath and 1 on the side through one of the snap-locks. Remove these.
4. Remove the 4 screws holding in the main board, 2 will be on the right hand side (as viewed from front), and the other 2 will be on either side of the heatsink. Unscrew the heatsink from the chassis, not the heatsink from the PCB!
5. Remove the 4 screws holding the transformer in place
6. The end of the unit should slide up and out of the chassis now, and you can open the clips on the front panel and slide the whole assembly out as one piece.
7. Replace the cap and re-assemble in reverse order.

Good luck!