can you beg or borrow a larger capacity power supply to try, as it sounds like either one of the voltage rails is faulty or when everything is plugged in it is over capacity, and shutting down.

Have you checked ALL the fans are working including the PSU one? I had a faulty PSU fan that would stop randomly after a few seconds, and the PSU would sense that and just shutdown completely. It was only when I had everything stripped that I noticed the shutdown was immediately after the fan stopping. Swapped the fan with a case fan and all was then fine.