The damage you described should not have occurred from the event. At least not normally. All motors should have stopped as soon as the props hit. It sounds like either emergency motor shutdown didn't happen, or the ESC shorted very quickly and the short was somehow self maintaining.
Another possibility is a fouled motor. I did see something similar once when a motor got fouled under power. It melted lots of stuff around it, and was in full "meltdown" mode until I got to it to turn off the switch. That one didn't damage the battery, but it was on the ground just a few seconds away from where I was standing. In a way, I suspect this more than a failure of the emergency shutdown feature.
Was the motor smoking, or still trying to run, when you reached the Q500 just after the crash?
Is there any evidence of melted plastic?
When you plugged in the new battery, did the smoke start BEFORE you tried to start motors?
Does the motor turn easily by hand when compared to the others? (It's normal to be a LITTLE bumpy as it passes the magnets)
Your actual question was "One or All". Normally, the answer would just be one, but this event took a different path. You could take the top shell off, de-solder the main power wires to that motor, unplug the ESC control wire to it, and see if you can test the other motors with the GUI. That may help understand if other motors were affected by the event.
Also, it is not a good idea to plug the battery in again until you have a handle on the issue. And certainly not while indoors.
Can you upload the telemetry file from the ST10? I would love to see this one.