Dim light on charger

I have a 2013, 15" MBP. Yesterday it was plugged into the charger and when I got home it had the strong green light, but was closed.

When I took the Magsafe cord out of the laptop nothing happened and the computer remained off. Pressing the power button led to no sounds or response.

Upon plugging the cord back in, the strong green LED flickered continuously and over the course of a minute or so, slowly faded into a dim green light, without charging the laptop at all. Taking the Magsafe port out, I tried it on a friend's MBP and it began to glow strongly straight away. Back into mine and it was fading.

I've tried a SMC reset and there was no change, however I think that it may be out of power and can't charge. As of posting I haven't had the opportunity to test with another magsafe cord.

I've checked the pins and they're functioning properly, there's no debris in the connection.

I've booked in an appointment, I didn't know if there were any home remedies I should try.