MacBook stopped charging after battery depletion

Hi there,

 

I drained the battery on my five-year-old MacBook one evening while working...to the point that it shut off on me.  I then did not re-charge it immediately, nor did I start the computer up again for several weeks.  I thought, "Eh, no big deal, I'll just plug it in and let it charge up again when I use it next time."  Well, I just plugged her in and now the charging cord is lit up green as though the battery is completely charged, yet the battery indicator at the top left of the screen says (Not Charging.)  Also, if I unplug the battery charging cable, the notebook shuts completely off.

 

Any suggestions or ideas, as I have NEVER had battery charge issues with this notebook before?

 

Thanks for any help you may have to offer.

 

J. Rowland

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