Computer shuts down after a while

My computer shuts down after a while I turn it on. I recently changed the Power Supply Unit. Then the problem was still there and someone recommended to get a new RAM. But the problem is still there.
When I try to play a game (Football Manager 2010) the computer just shuts down without a warning. If I just surf the net it shuts down after a while. I cleaned the dust in it so it isn't that either. I formatted the computer and re-installed Windows as well. What should I do. Can anyone help me please?

I have:
- Windows XP
- AMD Athlon 64 Processor 3300 2.41 Ghz
- Nvidia GeForce FX 5600XT
- 1 GB Ram
 
Usually, when a computer completely shuts down out of nowhere, there is either a power supply failure or a critical fault with the memory or motherboard. What are the specs on the power supply you installed and the RAM? It will also be helpful to list the complete specs of the motherboard as well such as make and model.
 
check the cpu temperature when it reboots go to bios/ health and check all the temeparutes or install any cpu temperature meter it will show you if you cpu is heating too much
 
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