''Lights don't tell the whole story'' - look under '''System Profiler:Power''' for charger status and battery status ''(what the battery circuit board informs the computer about it's condition)''. You could have a damaged or faulty battery connection or power circuit. ''I've seen a cracked battery do this'' - something was piled on top of the laptop (while it was in a case in an overhead bin on an airplane) and cracked a corner on the battery so flexing the laptop, putting it in or taking it out of a case, could cause the problem to appear/disappear.
''If this answer was helpful'' '''please remember to mark it accepted'''.