My brothers PC keeps turning itself off after a few seconds, he cleaned out the dust and changed the psu.. whats the deal?

Are all the fans working?

This usually would indicate that the processor is over heating

Yea the fans are working,the unit is completely dust free, new more powerful psu...

Did the problem only happen after installing psu?

I would go for a more better cooling fan for the CPU... it's always better to go above the CPU'S GHZ when adding a cooling fan/system.
For example if the CPU is 3.3 GHZ I would get a cpu cooler that will go up to 4.0 GHZ, though it's easy to install a liquid coolant system as they are more better.

A bad power switch or motherboard can also lead to this behavior. Processor overheating normally results in a lockup, reboot, or instant processor failure. Recent processors will also throttle their clock rate to avoid overheating in the event of reduced fan/heatsink performance or failure.

When the computer is booted cold after sitting overnight, how far does the boot process get before the machine shuts off?

There might be a temperature readout somewhere in BIOS.
If you can get that far.
Hit delete on boot then look around.

The temperatures should be <60 with no load like in BIOS.

How knowledgeable are you.
Does it get to loading windows/OS?