Have you tried replacing the battery connector? It's a cheap part, and worth a shot. They do occasionally go bad and cause various issues. Just search eBay for "A1150 battery connector"...there's one out there now for $8.08 shipped.
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Also, I know you said the battery is almost new, but do you absolutely know it is good because you've seen it charge in another machine? If you haven't personally witnessed it charging in another machine, you don't know for sure that it's good, and it could therefore be the problem.
Have you tried replacing the battery connector? It's a cheap part, and worth a shot. They do occasionally go bad and cause various issues. Just search eBay for "A1150 battery connector"...there's one out there now for $8.08 shipped.