My Computer is Shutting Down by itself.Can not find the problem

I am using an Home computer with a specification of following
Processor : Intel Duel Core 2.93GHz
Motherboard :Gigabyte G31
RAM :4 GB DDR2,Two slots of 2GB
HDD :LG 380 GB
CD Writer/Reader :LG
Microsoft Keyboard,Mouse and LG monitor with Windows xp sp3 OS Loaded in it.
I purchased this computer a year ago.
The problem started a week ago when i found my wires were cut in pieces by RATS.
So i purchased Monitor VGA in-out and power cable,CPU power cable A new mouse and New “VIP”(Brand) SMPS. I thought may be this time it will work but it did not my P.C starts for like 2 seconds but shuts itself off immediately.Please It would be very appreciating if someone could help me with this.Pls.ASAP.