Aspire V5 was shutting off usually when trying to log in (as if the battery was removed, with no AC).
Once in while it would stay powered on for a short time
When it did stay on, I found that pushing on the keyboard made in instantly shut off.
I proceeded to press different parts of the keyboard and found it would always instantly power off when I pressed on the right side of the keyboard only (especially near the letter L).
I removed the keyboard and eventualy found some damage (exposed copper and evidence of arcing) to the insulation for the keyboard backlighting (it's like a plastic strip with copper traces and LEDs in it).When the keyboard was pressed downward, the exposed trace would short on the metal plate behind it shuting down the PC.
I insulated it with a piece of tape and the problem was completly resolved....