Chosen Solution

As the title says, my MacBook is only charging with low wattage, there are two screenshots from coconutBattery attached. It might have something to do with battery, as the computer was not used in almost a month. A service provider has tested every component and they said it is a faulty battery. Have any of you had this problem? What did you do to fix it?

Update (10/04/2016) Apparently, the problem is within the logic board, the computer was dropped before and I guess some connections could have broken.

Did they try using a different mag-safe adapter? Apple OEM Replacement Battery Please note: this battery is difficult to replace and there is currently no guide. The battery cells are held in the upper case with strong adhesive. Use great care to avoid bending or puncturing the cells. Only use plastic tools when prying. MacBook Pro 15" Retina (Late 2013-Mid 2014) Battery Here a link to a last resort if we can’t figure it out: https://support.apple.com/mac-notebooks/

First I would make sure the MagSafe chargers cord and connector are in good shape often charging problems are related to a damaged cord or connector. Do you have any cuts, bumps or exposed wires in the cord? If you do you’ll want to throw the charger away and get a new one. Next I would clean the contact surfaces of both the charger and the computer with a slightly dampened cotton swab (Q-Tip) with isopropyl alcohol making sure the contact surfaces where clean. Also inspect them for any damage to the pins and the contacts look shiny and the plastic not melted. If not you’ll need to replace the adapter or DC-In board. If these are both OK, I would then reset the SMC following this Apple T/N: Reset the System Management Controller (SMC) on your Mac. Hopefully that fixes things.