Dead MacBook? It won't turn on, it won't show any "life signs"

Hope someone here can give me a light.

I have a Macbook Pro Model A1278, bought in late 2012.

The only problem I had with it once it was about a year ago I think, where I left the battery completely die and it wouldn't turn on or charge. (to get it back to working, I did the thing where you open the macbook, unplug the battery, plug in the charger, unplug it and then plug the battery again. After this, it was working again, charging the battery, etc).

Now, the current problem: about a week ago, it started to shut down by itself, even only during light tasks like using the internet. Every time this happened, I had to do the whole thing (open it up, unplug battery, etc etc) again, otherwise it wouldn't turn on (the light on the charger was a low green).

I suspected there was something with the battery that was making the macbook get too hot, so I decided to take it out and use it with the charger plugged in. After that, it worked perfectly for about 4-5 days. It stopped heating up and shuting down.

Until it shut down again, without heating up at all and now it won't turn on anymore.

When I plug in the charger, I get that really faint green light and nothing. No sign at all. Already tried different charger, tried turning it on only with the battery...

I know I have to take it to an Authorized Service, but I would like to get a light on it before I have the time to (only later next week) so I can prepare myself for the hit ($$$).

Also, last july I did an upgrade to it. Upgraded to 16GB RAM and took out my optical drive to add a hard drive (put ssd as system and the original hdd as extra).