Question PC freezes and gives no signal video after light touches

May 24, 2021
ASUS Z370, i5-8600K, Radeon RX 580, 16GB RAM, PSU Corsair 650W.

For a while now I've been experiencing freezes if anything slightly touches the computer case while the computer is running. Sometimes it might not even be a touch, a while back I placed a glass on the table and it froze.

After rebooting, the mobo led signals doesn't show anything out of the ordinary, but none of my displays receives any input. I'm able to use a software that shares mouse/keyboard with another computer while all screens on any cable on any input gives no signal.

After a while or a lot of restarts (including turning off the PSU), eventually, the displays starts working again.

I had something similar happen before while playing EuroTruck on 3 screens (which is not optimal with this GPU but it works) but it happened only on a driver version, after I downgrade the driver and later updated to a newer driver, it never happened while playing.

I think it might be the GPU (because it only affects video output) or the PSU (it is the oldest component of this build) or it might be something even worse. Anyway, I didn't find anything on the internet about this, so I'm trying my luck here. Should I replace something or is there a most likely fix?