Why won't my computer turn back on or charge?

I have an old 13" Macbook Pro that stopped working a while back and has been sitting in my room since then until I was able to deal with it. I finally was, as I wanted to get it back up and running (hopefully) so my Mom could use it because her computer (HP) is absolute crap.

I assumed that it was the battery that was the problem (again, it was a long time ago that this stopped working so I don't remember exactly what happened) but when I purchased a new battery from here last week (I got it in the mail Tuesday) and put that in I was able to boot it back up. I was thrilled! It booted with 50% battery charge also, which I found strange because I was sure that it died on me. Guess not.

With that 50% I erased my files and set everything up fresh then made an account for my mother. When I finished all that the battery level was 4% and I knew for a fact that I did not have a working charger, so I purchased a new one of those too thinking that that was all I needed and I would bring it home and be able to charge things up no problem.

That was not the case.

When I got the charger home and out of the packaging, I hooked it up to my MBP and the indicator light came on green, and stayed green. It never went to orange to indicate that it was charging like it should. It blinks a green light (at times I thought I saw orange, but maybe that was just my mind playing tricks on me or wishful thinking) for a beat (maybe 6 or so flashes) then the light goes out, then it starts this process over. (Also, while doing this there is this faint clicking with each flash of green, which I thought was odd.)

I went to the web and tried to find a solution to this problem (tried resetting PRAM, SMC, safe mode, holding the power button for 10 seconds, cleaning the charger prongs and the charge port, disconnecting the battery and reconnecting it again) but I got nothing and am just about to lose my mind.

The only thing I can think of is that when I was cleaning the charge port it looks a little scratched up on the inside, and it did spark once or twice when I went to plug in my charge cord. So I was wondering, is there any point in buying this part or might it be a problem somewhere else? With the logic board? (Honestly, I had never heard of that before now, so I'm not entirely sure I know what the "logic board" is.)