Power up computer for it to power down within seconds and the on/off swt to flashes on and off.

Possibly overheating, tho' I've recently cleaned all the fans, the PSU doesn't feel overly hot, neither does the motherboard.

It's a TINY machine

Any ideas how to narrow the problem down

Really don't understand question

Power up computer for it to power down within seconds and the on/off swt to flashes on and off.

Just a little more info would help on exactly what is happening

I would try these things

If you know how to get into BIOS (don't know about tiny but its usually Del or F2 or F10 or Alt+F2 while the "Tiny" logo is up. See if the computer shuts down while in there and you can take the time to check the temperature readings and post them + the processor model.

Try starting in safe mode (F8 immediately before the windows loading screen comes on). It could be a dodgy driver, if it works in safe mode then uninstall the most recent thing or do a rollback.

Try booting with no expansion cards (if you have any). And to check RAM (if you have more than one stick), then boot with just one stick, if it works add the next stick and repeat if it fails then that's the problem.

PS. Did it start after you cleaned the fans or before, you could have simply put the fan on the wrong way round. Make sure the side with the blades exposed is facing up.

Problem sorted, power supply gone plus video card, thanks anyway