I have a Librem 15v4 and I use the HDMI port to run an external monitor. It was making intermittent connection, so I bought a new HDMI cable, but that did not fix the problem. If I accidentally bump the HDMI cable, it will almost always lose the video signal, so I have to wiggle the cable. I’m wondering if it’s a loose connection where the HDMI connector attaches to the motherboard - or something else. Anyone else having this issue?
This took me back to a issue I had with a old HP 486 and again with a Dell laptop (model is forgotten). The Dell did the same things you describe. I found the tear-down fore it, and went to work. I found the problems was a cold-soldered nipple. That is, on the underside, all the soldered joints looked good. With meter, I tested each one for the VGA back then, and as I put pressure on one, it showed no connection, but if it put pressure from the other side, it showed a connection.
I pulled out my soldering gun, remelted the solder, put all together never had another problem.
I also had a IBM 8 bit - yup before 286’s. And when I’d boot, it would sometimes err out. I did the same; measured every nipple and found a cold -solder. A meltdown on the nipple & I had no more boot problems
Could a cold-solder be your problem?
p.s. I once found a Dtop’s CPU that had 3 corroded pins. The computer would start and was OK, for a while. Once the CPU heated up, I gather there was enough corrosion and expanding in the heat, as pins will do, we’d lose the CPU to some pretty wild goings on. I thought it was haunted 
I sent it back and got a clean one.
~s~
Cold solder joints are what I was thinking as well, since I bought a brand-new HDMI cable and that didn’t fix anything. The next time I open up the case I’m going to have a look, but that’s going to be a while because of a coreboot issue: if I reboot the machine, everything is fine, but if I shut it down the next time I start up I might have to wait 2 hours for coreboot to see the NVMe SSD.