MacBook Pro turned off and won't turn on!

I was just using my laptop normally when suddenly the whole computer just shut down. I turned it back on straight away and it was fine. Another hour passed and it did the same thing. I could also turn it on again. And then it happened again, this time I couldn't turn it back on!! I have never spilt any liquid over my laptop so it isn't liquid damage. I have tried resetting SMC, replugging the battery cable inside the computer, leaving the charger disconnected from the mac for a few hours, nothing works! The strange thing is when I have my charger disconnected and I press the little button on the side to show power, nothing happens. But when I do the same with the charger connected it shows full battery.

I have a MacBook Pro 15" Early 2011 running OSX El Capitan.

Your Mac should still be able to turn on with a dead battery. As long as charger is functioning properly, it's more than enough to both power up and charge your Mac.

You have three possibilities for the cause of this:

MagSafe Board (highest probability). This board is known to go bad and when it fails, it presents symptoms similar to what you are describing. The good news is that this component is very inexpensive ($10-$15).

You said in your post you had opened it up and disconnected/reconnected your battery so it sounds like you have the tech skills to do this repair.

Your Charger (medium probability). This is the easiest test to do. I once took in a MacBook Air into Best Buy and hooked it up to a charger they had connected to one of their display models to verify that the charger wasn't the problem. It may or may not be the charger, but there's no need to spend $60 - $100 just to test it out. if your computer comes to life after plugging in another charger, you have your answer.

Your Logic Board. (least probability). This is obviously the most expensive, but most of the time, it's not the issue. The only way to diagnose this is at the component level. If you have exhausted the first two possibilities, it's time to send it in for a professional diagnosis.