By chance did something spill onto the system or did you sit the system down on a wet surface?
I would start off by downloading this little gem of a tool to see more clearly what is going on [http://www.coconut-flavour.com/coconutbattery/|coconutBattery]. Tell us what it tell you.
I suspect you likely have some corrosion on the main logic board around the FET's or one of the FETs is failing. Look between the fans the five pin'ed devices are the FET's (4). Here's a good image for reference [http://d3nevzfk7ii3be.cloudfront.net/igi/5X1JGJETlTmgkhcc|Logic Board]
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== Update ==
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Well some good news here SMC services area working and the Battery is in good shape.
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The bad news is it looks like the charging logic has a problem on the main logic board. As you suspect liquid damage I think you need to do a teardown of the system to repair or replace the keyboard and clean up any spillage on the logic board (both sides). You'll need distilled water (not tap) and high grade of Isopropyl alcohol (85% or better). Some cotton swabs (Q-Tips) & a soft toothbrush to scrub some areas. First remove the battery and then use the distilled water on any stained areas to clean up the corrosion afterwards go over the same areas again with the alcohol to clean any oil or grease and to act as a drier to help in removing the last traces of water. Make sure to let the system dry out a good day before powering up again
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For now lets pop off the bottom cover and inspect the FET's and the charging circuit which is located between the fans. Do you see any corrosion or damage using the picture I gave you as reference?
By chance did something spill onto the system or did you sit the system down on a wet surface?
I would start off by downloading this little gem of a tool to see more clearly what is going on [http://www.coconut-flavour.com/coconutbattery/|coconutBattery]. Tell us what it tell you.
I suspect you likely have some corrosion on the main logic board around the FET's or one of the FETs is failing. Look between the fans the five pin'ed devices are the FET's (4). Here's a good image for reference [http://d3nevzfk7ii3be.cloudfront.net/igi/5X1JGJETlTmgkhcc|Logic Board]