Yeah, I guess my next step is to take off the fan and see if I can spot anything wrong with it. And it's a continuous clicking noise as long as it's plugged in. It was looking like it might have been coming from the fan because it was trying to spin up. But the screen and the Pi Zero are totally black and not powering up. (I think it's a pi zero that that screen is sitting on.) But honestly, I just woke up. I'm going to caffeinate first and see what I can see here in a few minutes.

^ Yup usually power issues. Switch mode power supplies when feedback is unstable (high load, poor regulation due to failed passives etc) will flap output power. Usually it's on the output/secondary side but cheapo import power supplies have been shipping with half wave rectification and shitty caps in my recent experience.