Well, you’ve got a few problems here!
First the battery is on its last legs as its close to the end of its expected life of 1,000 cycles. Some batteries don’t make it to the 1,000 so its possible its running on vapors now!
The charging logic and your MagSafe charger are not working properly! As CoconutBattery is telling us the charger is connected the charger its self is not charging the battery which is should be given the batteries current state of 17.4% charged Charging with 0 Watts!
At this point you’ll need to look for corrosion around the SMC logic. Follow this guide to take it out MacBook Pro 13" Retina Display Late 2013 Logic Board Replacement and inspect both sides for any spillage or corrosion or any damaged components. Make sure the sky blue area which is the SMC chip and its supporting logic is all clean on the backside of the logic board.
Well I can’t see any signs either, so that leaves only one thing left a knockoff charger which has damaged the voltage comparator resistors! Here’s a good explanation from Louis Rossmann How cheap eBay batteries DESTROY Macbook logic boards! While Louis is describing the Unibody MacBook Pro’s SMC the same logic is used in the Retina models (its laid out a bit differently)
At this point its time to visit someone with the deeper skills to fix your logic board.
Here’s some additional info:
● Don't Replace Your MacBook Charger With a Cheap Knockoff
● OEM MagSafe Chargers vs Cheap Imposters: Teardown for Truth
● Lacking safety features, cheap MacBook chargers create big sparks
● FAKE Magsafe MacBook Chargers on eBay - Watch before buying a Mac Charger
Sadly, it is very hard to tell which is which from the outside. We used a scale to measure the weight as the best way. Using a known knockoff which is lighter in weight to compare with the others we had. We had hundreds to check!
Make sure you bought your charger directly from Apple and its in its original packaging.
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Let’s get a better view of things, install this gem of an app! CoconutBattery take a snapshot of the apps main window and post it here for us to see Adding images to an existing question
из Dan