If you are putting the computer to sleep by closing the lid the root cause may involve a short in the LCD connector. You should definitely mention this when you get it repaired again.
It is doubtful that any connected device, battery or charger is the root cause since you used the computer for several hours. Had any of these caused the failure it would certainly have occurred before you put it to sleep. However if you closed the lid to put it to sleep that might have triggered a short. Perhaps an extreme static discharge could be responsible but I'd imagine that you'd have mentioned shocking yourself.
The root cause of the mother board (logic board) failures is due to a poor design. PERIOD! There is not much someone can do to screw up a mother board. Just think about it. How many computers do you know about that have logic board failures? I can't think of any except for Apples'. This is not a matter of how you turn your computer off; whether or not you put it to sleep or close the lid. It's an inherent design flaw. They screwed up and they are covering it up.
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I have logic board problems too. I have had a late 2010 mac book air for 2 and half years. Its been a great machine in general - although it did go back within the warranty period for the track pad
Now it has logic board failure - symptons are the sound going and the battery is dead and it is unable to charge which means every time you put the power lead on the computer thinks it is starting from scratche.
I have been quoted over £400 for the repair! Like the above post I do not believe that this part should fail - and if it does then it is a major design problem and Apple should be doing something for us. I just dont know where to start.
I have used macs for 14 years and owned eight along the way. Most have them have lasted many years with full functionality the record was my G3 imac which was still working after 13 years.
I really cant believe the situation I am in and rather think I have bought my last mac!