I got my Framework (AMD 13) today and put everything together, but I was just getting a black screen on boot (not blacklight, no logo, nothing). I let it sit for 30-45 minutes thinking it was memory training, but also after rebooting again nothing happened.
I had originally installed two RAM sticks, so I tried removing the RAM from the second slot. Afterwards it booted just fine within 1-2 minutes. I then tried putting the removed RAM stick into the first slot and everything still worked.
I think it looks like there are some bent pins in the second RAM slot (see the 4th & 5th pins from the bottom):
They test the laptops before shipping (at least I remember watching their assembly video of the factory line). Whether they test both slots is hard to say.
It is also possible they were bent when installing the ram. Fortunately they are a form of spring steel that is designed to mostly retain its shape. Similar to the “pins” on a PCI card slot. They expand around the edge of the contacts on a card when inserted to make contact evenly.
You did the right thing by contacting support and taking pictures. IF support is ok with it, you could carefully use a pair of tweezers to gently push up the pins a little to see if they will form back in place. A safer item would be a toothpick (nonconductive); though I would be concerned about it breaking off and really jamming up the slot. You can see from your photo that the 7th and 8th pin are shorting together or likely were at one point.
If you can get the edge of the ram underneath the malformed pins as it is gently pushed into the slot; they should straighten themselves out. I would think they should hold themselves in-place nearly indefinitely. If both slots work after you were to try that, it would be a fix without having to go through replacing the motherboard.