The problem came back. I tried switching out the power cable with the one I used in testing last time, and it was to no avail. At this point, I am going to do more testing to determine if this is an FM-only problem and/or if this is a VHF-only problem.
(1) Scratchy receive on 2M FM. Haven't tested other bands or modes. Scratchy-ness sometimes goes away in a sudden fashion (like flipping a switch). It's very much like a bad connection.
(2) Low audio volume
Potential Solutions from Research
Tighten chassis screws
"there is a known problem where the power connector is very close to a component (part of the 2m bandpass RX filter) mounted on the board. So close, that it can be knocked off the board when the power cable is plugged in or removed."
"Make sure the faceplate contacts are clean. Mine goes dead a couple times a year in my truck from this."
From AB8SH (local friend):
Check the power connection. The Molex connector used by Icom is frequently problematic.
From unnamed (and increasingly difficult to find) posts on the IC-706MKIIG Yahoo Group:
The power connector has been mentioned multiple times on the IC-706MKIIG Yahoo Group. Additionally, the ground clips have been commonly mentioned. Frequently, these are mentioned with the 17m oscillation problem.
First thing I checked was power and ground connections. The ground clips (that should connect to the case) weren't putting a lot of pressure on things. I bent all of them up towards the the case for good measure, although I'm not sure that fixed anything. I also ensured that all the internal screws on the PCBs were tight (all of them were).
The speaker looks aged (heck, you can see UV discoloration in the cone). Otherwise it looks fine.
After putting the rig back together, I put it on the radio bench connected to a DIFFERENT power cord and it seemed fine. A few days later, I mounted it in the truck. After driving a few miles and getting stopped at a long traffic signal, I decided to tilt the rig up more (yes, I had an appropriate Philips head screwdriver with me) and while being stopped at the light I quickly unbolted the front two mounting screws and tilted it up.
The radio died.
I (still quickly) finished bolting in the radio and while stopped at other traffic signals attempted to jiggle the power connector in the back to no avail. When I got to my destinations (another ham's house), I found that the plug came out. In subsequent testing, it seems everything is fine.
So What Was It?
I'm banking on a bad power connection. That being said, any mobile setup should probably include proper securing of power connectors and ensuring that road vibration won't cause things to come loose.
Edit: It is likely the power cord. I noticed static since posting this, so I'm going to replace the power cord and check the pins on the current one.