|When you first supply power it starts for a second then shuts down? This is normal. The machine is in standby.|
If you are not using a surge protector ...going through the normal shut down and then shutting down all power from the wall switch is something I would recommend. This prevents waking up in the morning and finding a toasted system, because of a surge in the middle of the night.
I would press "control alt del" and see whats process is running to lock up the computer. Is it the mouse that's locked up or the keyboard as well.
I would then make a list of the sites that lock up the system and determine if it is the site by visiting a few times.
If random then there is a problem on your end....as it may be a driver thats not working as it should.