Won't run more than a minute

Win 7 Ult
....................

I had used this as my primary machine. Onboard video had died, I installed a new video card, I then had a starting problem, but I don't know if the 2 events are connected. A few people worked on this problem at SevenForums, but without results. Would like it to be my backup machine if I can fix it.

SPECS
Win 7 Ult, had been a refurbed Vista.
64-bit Multi-core 2.60 gigahertz Intel Pentium G620
Board: PEGATRON CORPORATION 2AC2 2.00
BIOS: AMI 7.16 10/05/2011
HD ST3250310AS (250.00 GB)
DVD drive
6 GB RAM not sure of type. Whatever we used in 2010.
BIOS: AMI 7.16 10/05/2011

Symptoms.
Runs 30 seconds to one minute, with all 4 fans going and HD spinning, then it dies. Doesn't run long enough for the BIOS or monitor to start. Sometimes it doesn't start at all.

What I've tried--one at a time between trials
Removed all dust
New PSU—0 difference
Changed the HD
Isolated the start button and it works fine.
No cables are unplugged
No bloated capacitors
Pulled and reseated all cards, cables
No visible signs of damage or bad wires (not accounting for invisible)
No beep codes. Doesn't run long enough to beep?
Changed the CMOS battery


Is there a thermostat that could be telling the mobo that there's overheating? That would account for gaps of time between successful trials.

It is possible that a thermal sensor is reporting an overheating condition and shutting down. This would likely be the CPU thermal sensor, but it could be a video card sensor.

One easy test would be to remove the video card and see if it still shuts down or stays running. It does not actually need to show anything on the screen for this test. If it still shuts down, we have eliminated the video card as the source of the issue. It would then be time to check the CPU fan AND thermal compound.

The new video card has its own fan, and removing it doesn't help.

Re: the screen. There is none, it doesn't stay on long enough to engage the monitor.

There are a few very fine squiggles where there's no paste or maybe it's thin. Do I need to buy paste now?

Fan is clean

Normally, 30-60 seconds should be enough time to at least get some BIOS messages on the screen. However, if the CPU did not have much thermal compound between it and the CPU heatsink/fan, that could definitely be your problem.

Possibly useful links:

https://www.tomshardware.com/reviews...on,5108-3.html

https://www.ifixit.com/Guide/How+to+...rmal+Paste/744

https://www.intel.com/content/www/us...mal-paste.html

https://www.youtube.com/watch?v=hNgFNH7zhQ

Did the thermal paste. No change. It's something we can't see.
I'll use it for parts.

and thanks for your time :-)