Hi!
There are a few things to try.
1: Replace the PIN connector and see how that goes, you already did you said, it's not normal that it boot without pressing it down, but won't be issue regarding you have now.
2: Do a complete re-cap and see how that goes. It could solve the glitchy screen.
3: Try a new video cable and see how that goes!
If the above failed, then it's something else on the motherboard and could be a lot of things. Most likely that the CPU went bad...