Windows 7 HP Desktop Keeps Shutting Down Randomly

Basically I have an HP Pavilion a6230n desktop. It's about 5-7 years old now. The specs are AMD Athlon x2 5600 processor, 3GB of Ram, nvidia Geforce 6150 SE nForce 430, 15-in 1 card reader and light scribe cd/DVD drive. It's operating system is windows 7 professional 32 bit at the moment (before my reinstall last night, it was windows ultimate 64 bit) and the computer came as a factory default of windows vista 32 bit.

Basically for some time now (4 months now) my computer has been shutting down at random times wether it's being in use doing little things such as watching videos, browsing and etc or being on but not being used. I think it is not a overheating program because At times, i have let the computer to cool down, before I boot it up and wether it being on for 5 minutes, it will shut down randomly. Even at times while the computer is booting up as soon as the windows 7 loading screen is gone. It will shut down.

I have tried steps like checking to see if the power cable is properly connected to both the CPU and outlet and have tried removing external USB cords. I have tried re installing windows 7 last night and the outcome is still the same. But what I've noticed is after I have re installed it, the shut downs are occurring more. Not sure if its a hardware issue or hard drive issue but apart from that, the computer is fine. Still runs fast up to par as computers nowadays and etc.

Any thoughts and ideas will be much appreciated.