The age has nothing to do with it but it does look like the power switch may be faulty.
With the pc being over 5 years old maybe the Power button is causing this?
Highly doubtful since it has been running for 5 years.
I can't think of anything else other than that or a shortcircuit which is corrected by laying the motherboard bare on cardboard.
Could that somehow cause the freezing/reboots for some reason if the buttons bad?
I would say that it most likely is the power button and possibly a wire that is either loose or maybe frayed that is causing the issue.
I've pressed that power button a million times before. Could that somehow cause the freezing/reboots for some reason if the buttons bad? I have an identical power button that came with the custom case I could try
Yes just to make sure.
Should I try adding parts back to the system one by one and see what happens?
Since the system started and ran with your memory outside of the case with no problem I don't see the memory as being the issue. Your freezing outside was caused by the heatsink not being properly installed and you corrected that as you stated earlier. The system ran fine then.
Or should I be testing ram with Memtest, or cpu with some other software? Any ideas? I'm so excited that it worked for a bit!!! I shut it off for now.