A computer randomly turning itself off when under load is usually thermal problems (ie your processor is overheating) or your power supply is dying. Saying that you went the route of replacing your power supply I would say the reason your computer has been turning itself off is to try to protect itself form an overheating processor. The fact that it will no longer turn means that you may have damaged your processor, motherboard, or both. A shot in the dark to see if you can get it to turn back on would be to unplug the tower, and remove the battery in the motherboard. Leave the battery out for a few minutes and then reinstall it, plug the tower back in, if your new psu has a switch in the back make sure its in the power on position and try to start it. If you can get it going we can guide you through a few tests to make sure your temperatures are not causing issues.