Windows 7: Toshiba Satellite L305 not bootable if power cord is plugged in

I have a laptop with Win 7 HP 32bit SP1, which doesnt boot at all, if the power cord (AC Adapter/Battery charger) is plugged in. Further if power cord is plugged in after booting, the system hangs / shuts down. It runs fine on safe mode. I believe it is a driver updation problem but not sure. I have updated all drivers given in Toshiba download site. Any suggestions?

Hi ahimsasoldier, Welcome to the forums ,Have you access to a different AC adaptor ? that you can try to see if the one you are using is faulty
You say you have updated all the drivers from Toshiba website and you still have a problem did you check the Ram using "memtest" ?

I dont have access to any other adapter. Secondly, I dont think the problem is with the AC Adapter, since in the safe mode the system works fine with the AC Adapter (Battery charger) plugged in.
How to run the memtest?

I dont have any other AC Adapter. I dont think the problem is with the AC adapter, since the machine works fine in safe mode, even with the adapter plugged in.
I have run the Windows Memory Diagnostics test and there are no problems.