Laptop turns off by itself (only when in OS)

[VirtualPenguinGaming]

Specs:
CPU - Intel Core 2 Duo T8100
RAM - 2GB DDR2
Hard Drive - 60GB 5400RPM HDD (I swapped out the original 320GB 7200RPM for that)

The laptop works fine in the BIOS, but just as I get into an OS, it seems to crash. Sometimes, it stays fine without turning off for about an hour until I need to recharge it, but most of the time, about 3 minutes into an OS, the laptop shuts off instantly with a loud sound like a PSU turning off suddenly. I know it is not a virus or anything like that because I installed different operating systems such as Linux Mint and Windows 8, which did not fix it.

Another thing is that when I plug it in while it is on, the laptop shuts off. When the laptop is charging and I try to turn it on while it is charging, it turns on the fan and instantly turns itself off.
Anyone got ideas?
The way it turns off is forcefully, not a normal shutdown.
This is not an overheating issue. I cleaned the fans recently and there is no dust buildup.

 

[mdd1963]

If you have another battery you can try, that will rule out the simple. If it's not a bad battery, you are left with mainboard, or, essentially a junked laptop at todays prices unless you can find someone selling one with a bad screen for cheap...

 

[VirtualPenguinGaming]

If you have another battery you can try, that will rule out the simple. If it's not a bad battery, you are left with mainboard, or, essentially a junked laptop at todays prices unless you can find someone selling one with a bad screen for cheap...

It is not the battery. I have tried without the battery and then the screen goes crazy with weird colors popping up around the screen. Its probably the mainboard.