MacBook Air won't boot with full battery, unless additional "2 min" kick-start adapter charge.
Sometimes my MacBook Air 2010 doesn't boot (doesn't show any sign of life, no screen, sound, etc.) even though the battery is fully charged. Only after I plug in the adapter for about two minutes it does boot. In this case I can disconnect the adapter immediately afterwards and it works fine, say, 7 hours, and I can shut-down and boot several times, indicating the battery was fully charged already and is healthy. This is frustrating when taking the laptop with me outdoors, because this means its useless and unreliable (usually it boots fine!). Help me please!
I've tried all possible alternatives listed here:
http://news.softpedia.com/news/Things-to-Do-if-Your-MacBook-Does-Not-Turn-On-133 615.shtml
(Based on this: http://support.apple.com/kb/TS1367?viewlocale=en_US)
Many thanks in advance.
MacBook Air, OS X Mountain Lion (10.8.3)