This problem is common on all notebooks.. Known as bad or open solder joints. The repair requires disassembly of the unit, And the resoldering of the connector to the board. (Sometimes also replacement of the connector). If you are an avid solderer and have no fear of tearing the unit down this isnt too complicated a procedure.. If you need help feel free to ask!
Therefore I lose power constantly and the notebook immediately goes into hibernation. I'm switching wall outlets constantly.
A Warning message always tells me to switch from battery power to AC power, but the AC adaptor is already plugged into the wall.
The battery is always colored green, so I don't think there is a problem with the plug and battery connection. I think the problem exists between the AC adaptor connector and the actual computer.
Could I replace that connector and its adjoining connections? BTW The connector also feels a little loose. It's not normal I'm assuming.

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