Dim green flickering charger light

You may need to replace the magsafe DC in board.

 

If you have tried a different power adapter, and the battery, too - the next step would be the magsafe board (the internal part that provides the magsafe connection to the logic board.

922-9307 Magsafe board. It's not too bad to replace. iFixit.com would have a repair guide for that.

 

Before ANY other 'drastic measures' are taken, have you Cleaned the Connector on the computer..?? THe light is indicating that a Charge is occurring, and given that Resistance will lessen that Voltage transfer, it is more than possible that some corrosion (or coating of fuzz/ cola/ goo) may hinder that!!

An old toothbrush and some Rubbing Alcohol will most likely tell the story.. if a bunch of 'black crud' comes off you will have the answer _ and it is does happen to have a coating of Soda Pop on it, some warm water (small amount of toothbrush/ Q-Tip) will break that down far better than a $25 can of Contact Cleaner _ No matter what, LESS is more when doing this _ we are talking Small Drops, not Ounces, and keep at it with more clean water if dirt does come off!!

Other than that, if the machine has suffered any impacts lately, the Solder Joint on the connector board may also be loose (cold solder) and would require a qualified person to attack that, if so _ Good Luck, let us know what you find either way!!

 

This happened to me and it turns out that there was a piece of mechanical pencil lead in the port, which prevented the charger from making contact with the port. As @bobcan said, if cleaning the port doesn't work, a replacement or repair will be needed

 

** Also, it just occurred to me (as I read the above post re: mechanical pencil lead) that since the connector is literally magnetic, and fairly strong, so you may even have a small piece of ferrous material in there keeping it from contacting properly _ Take a peek, and hope it is something as simple as that _ somehow!!

 

Try resetting the smc

 

Yes, an SMC reset can be the fix.

Now, if the hardware reset doesn't make a difference, your list of possible fixes is getting very short:
magsafe adapter
battery
magsafe board - while inside your MBPro, you would check for corrosion or maybe evidence of a liquid spill (symptoms of liquid damage/corrosion can sometimes take weeks to appear - inspect carefully!)

finally, that's pretty much all of it, except you are left with -
the logic board.