MBP battery won't charge
It appears that you didn't fix the original problem which was why your MBP wasn't turning on in the first place - your battery wasn't charging so you had a dead battery.

You have already verified that...


the battery is good (it's new)
the charger is good as it works on another Mac
the logic board is good because when the battery has juice, it works.  


Now, it seems that since the battery has gone to 0% and the charger is plugged in, your MBP is dead, correct?

That means you Mag Safe DC In board is most likely shot.



This is fairly simple to fix (I am assuming you changed your own battery). iFixit.com has an excellent tutorial on how to replace this component.  The good news is that this component is fairly inexpensive ($11 on Amazon).