Won't run more than a minute

[foxy]

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.