Macbook Pro Retina 13" 2013 is completly out of charge and will not charge?

I have read other threads where people have suggested resetting something on the computer but I can't do that because I can't even turn it on.

I have bought a new charger, because I thought that it could possibly be a faulty charger but even with the brand new charger it still wouldn't turn on.

I have a Genius Bar appointment tomorrow morning, I've never been before and am wondering if anyone has any ideas on how much it would cost if it were a faulty charging port that they needed to fix? I got the computer in November of 2013 so it is still under warranty.

Thanks