Alienware Aurora ALX shutdown during POST

From the product support page :

Aurora ALX

 I7-920, 2.66 MHz

Nvidia 240 sometinsometin, cannot find more on the cards themselves

Shipped in 2010.

Basically, when the computer starts, the fans kick in high gear, the leds light up all over, the fans slow down gradually over a few seconds then the computer shutdown and restart the cycle.

I removed the graphic cards, HDDs and RAM.

When there's no RAM, I get a 2 beep code meaning the RAM was not detected, obviously.

With the RAM in and no video card or HDD, back to the start and shutdown problem.

I assume the CPU is ok since POST get to check the RAM.

Could the power supply be dying, or a problem with the BIOS, or could some thermal sensor be busted and act as if the computer is overheating?

Thanks in advance for your help.