Hi we have picked up an old hp pavilion t3000 desktop for our daughter to muck around with and basically get used to I.t. , we're now a BIT excited as it almost seems to be working, I'm only a novice myself .
What I've noticed is when this four pin type connection is unplagged everything comes on and stays on except the monitor, however if this cable is plugged in, the computer comes on for about ten seconds including a hp blue screen on the monitor with some options in the bottom right coer to press esc,f10, and others , but everything dies after ten seconds.

Can't seem to ATTACH pic, sorryWhat connection is this? You will need to describe it in more detail.Its apparently a atx12v, I've been googling....it's square and white and SORT of beside/below it is a long black empty slot, would this slot normally have a card in it?

Noticed something else too, it powered on then off , so I left it. JUst noticed the MOUSE is lit up? !? nothing else is on but the red light in the mouse...I'm sorry but the POWER supply is faulty and will need to be repaired. You could also replace it. The power supply is a standard ATX power supply which you should be able to get from any computer store.