Notebook/battery issue

This one has dogged me relentlessly.

HP Pavilion G6 notebook with Windows 8. System works flawlessly on the software side, the hardware, however-

The notebook recognizes the adapter about 60% of the time. If the battery is fully charged the adapter will usually be recognized, but if the battery is low it seems not to. Sometimes if I leave the adapter plugged in for an extended period of time (like overnight) and come back the power jack light will be on and working.

If I plug in the adapter and remove the battery it will switch over seamlessly, but if I replace the battery it won't recognize it.

Trying to boot without the battery works about 40% of the time. Generally I get 3 blinks of the light which suggests a RAM issue according to HP's website. But I've replaced the RAM several times to no effect.

I've swapped chargers to no effect.

I've replaced the jack in the notebook to no effect.

I'm considering a battery replacement, but it charges fine and lasts about three hours (so far) WHEN the charger is recognized.

Am I missing something?