Solved Computer Dies Upon Boot up

This morning I found my computer off; I thought that I had left it on last night. I know that the power didn't go off because I still have the clock on the microwave. So I tried to turn it on only to have it shut off after about 20-30 seconds without a beep and no video. If I try immediately afterwards it's only on for 1-2 seconds. I made sure that the power cables are securely connected to the motherboard but no change. I have made no recent hardware changes.

So what's the most likely cause? Is it the PSU, memory, heat, or is the motherboard dead? This is a custom build that is over 7.5 years old. I can list the parts if necessary.

I just timed it and it lasted for 50 seconds. I tried pushing in all of the cables, cards, and memory sticks. Nothing is loose.

To make things even stranger I unplugged the power cord and hit the power button. Then I turned it on and it booted normally. So what does that mean that the problem is? Is the PSU going bad?

EDIT: Just after finishing this post the computer shut off again after less than 10 minutes. I've been able to bring it back using the same method. I decided to run speed fan and the cpu is currently at 43 C well below the computer's shut off temperature of 75 C. I think that we can rule out overheating but I'll keep speed fan running.

Could be a bad power supply.

The psu itself is possibly overheating and popping, especial true if it is 8 yrs old too.

That's what I'm thinking but no further issues today.

I am marking this resolved because I am getting rid of this system. At times it works quite well and sometimes not at all. It has served me well.