MacBook Pro turned off and won't turn on!
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.