Well, Steven I owe you on this one. You called it right to the component. The short was on the 5V rail and the component was D108. That is sure a tiny little diode. Going to be fun to put a new one in.
Now the fun of trying to find a part number for that diode. The parts list only gives the specs, not a part number.
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A thermal camera is hands down the best way to identify a shorted component. Turn on the power and look for the thing that glows. You can get one that attaches to your phone for about $2-300.
A multimeter in continuity mode is the second best way.
First order of business is to test for continuity from ground to each of the three voltage rails. The 2x4 and 2x3 headers that the power supply boards attach to are good places to do this.
To map the drawing of JP101-4 to the physical layout on the board, look at the board from the bottom side, i.e. the side with the microprocessor on it, with all of the through-hole components facing away from you. Turn the board until the antenna connector is pointing up, and the DC input jack is pointing down. The solder pads for the headers are now in the same orientation as they are in the schematic. But don't trust me on this, use your multimeter to verify ground (the body of the antenna connector is a convenient place to test this from) and Vin (use the center of the DC input jack) at minimum. This should be enough to make you confident.
If you are seeing a short from ground to either VCC (the +5 volt rail) or VDD (the +3.3 volt rail), try removing the associated power supply board and see if the short is still there. If the short went away when you removed the power supply board, the likely culprit is a failure of D108/9, or one of the tantalum capacitors C106/7. If the short persists with the power supplies removed, you have had a failure of one of the many ICs on your main board, and it's time to decide how you value your time, money, and energy. Be aware that even if you find and replace the failed component, the same event could have damaged other components without totally destroying them, and you could boot up your radio to find that still more work needs to be done. I had this realization after I managed to make my QMX boot again by removing IC403, and weighed the cost of buying and shipping a replacement IC in single digit quantity, and ended up just buying another QMX. Maybe I'll use the old one as a source of spare parts for the new one if I manage to fry that one too.
If the short you're finding is +12V to ground, again try to see whether the short is in the power supply board or in the main board. Luckily, not too many components are actually hooked up to +12V, at least in a way that makes them liable to short to ground.
Based on your symptoms: The board stays powered after releasing the encoder, which means the CPU is awake and putting voltage on the PWR_HOLD line, which means that the 3.3V rail is good. But no display, and the display runs on the 5V rail. So I would say the issue is somewhere on the 5V rail.
