Desktop power drop out

Hello,
First let me say that I am new to this forum and no expert on computers, so please be gentle with me!!
I have a Dell Vostro 430 / i7 / H57 Intel Chipset /2 SSD / BIOS 2.4.0 Mini stack desktop, running Windows 7 Pro 64 bit.
This machine is 12 years old and has had;
a) a couple of motherboards replaced by Dell under a Service Agreement, which Dell will not extend.
b) HDDs changed to 1 TB SSD and 500 gb SSD a couple of years ago, following failures.

It has been a very reliable companion until a couple of days ago, when it just cut out as though we had suffered a power cut, [which we hadn't].
So I tried restarting it immediately- Booted up just fine and ran for a couple of minutes with only start up programs loaded, then cut out completely.
Left it to cool for an hour and repeated the start up. Exactly the same result- booted up as usual, [albeit a little slower than usual] and then a couple of minutes later just cut out.
Tried again in safe mode, [although no new programs or H/W installed], same result.
Opened up and re-seated the various cards/boards- NO Change
Removed the CPU Fan and Heat Sink for a thorough clean and blew out any loose dust & fluff and replaced, [noticed that there was no Thermal Gel following the last time the MOBO was replaced by Dell Tech- about 5 years ago]
Now it's worth mentioning here that we are relatively close to the coast and I have noticed that any unplugged USB plugs get a fair bit of surface rust if left unpacked/unplugged.
It's also worth mentioning here that over the past month, the CPU Cooling Fan had become very noisy and was obviously running on high speed from start up and not reducing in speed when I opened a program. I mention this as this M/C runs on 2.4.0 BIOS, which was a fix some years ago to resolve an issue of noisy CPU cooling fans at start up, which was supposed to drop the speed as soon as the M/C was set to work.
So what's wrong?? I suspect that the MOBO has developed a fault in the CPU Fan Control unit or sensor, because I can't believe that the PSU would cut out afetr almost exactly the same time every time the M/C is booted up.
However, that still does not explain why the M/C keeps cutting out a couple of minutes after booting up.
HELP!!!
DD

 

OK, with both drives disconnected and starting from a cold start, the computer screen showed no drives connected and requested to put boot media into a drive or reconnect a boot-able dive.
The CPU cooling fan started and continued at High Speed.
Then the computer Cut off completely after 3-4 minutes.

 

Tried booting off a start up disc.
Computer cut out after 3 min before booting completed

 

OK thanks for the response.
I'll get some thermal paste and try that.