Even though this may not apply in your case: Could the reason for the fault being that someone (maybe you) tried to connect a too large (in Watt) power supply which overloads the curcuit and causes an automatic shutdown. I have had this problem with my Dell Latitude D820.
I think that one problem is charging the battery and running the computer at the same time. I am considering to bring an extra power supply with lower wattage on the next trip as my laptop will run and charge using this PSU but will display a message that it is running on reduced speed.
The usual solution for this would be to remove your battery while you are using the laptop. I seem to recall in-flight magazines on some carrier actually requesting you do this. Of course problem is if the power dies you loose whatever you were doing.