Overheating??? Seriously, if your fan is not running, then chances are it'S overheating. Does it feel hot?
If so, let it cool down for a few hours, or until it's cool) and try it again. If it gets further, then this was the problem.
Also, it could be that the AC-in is broken, and it is not charging the battery. Check the battery charge light.
There could just be about enough juice left in it to give you 10 seconds before it dies again.
Or, the battery itself could be faulty.