I've got a few suggestions:
Before anything, I would recommend a warranty or replacement through the company on laptops before you dig around fixing for yourself, however if you have an expired warranty/dont care or want to fix it for yourself allow me assist you:
Remove the battery, charger, and hold down the power for 30 seconds to a minute do discharge and static power.
Is it humid where you live? Perhaps a bit of water got into the internals and is shorting the system?
Is the CPU cooler properly attached? Thermal paste?
I need to know this also:
Do you see any prompt on the screen when the system is on? any bios stuff?