ok i might have the solution.
a little background- the exact same problem happened to my sister and i figured it so it might actually work out.
The [Possible] Solution:
Have you tried to insert the cord into another AC place thingy.
Like say you are charging your MBP in your bedroom, try taking it to say the living room and plugging it in there.
i dont remember if i tried using my magsafe cord on my sis's computer, but i do remember taking her laptop into my room and charged it there and it worked. all my sister had to do then was use another AC "place" and it worked!
Another thing i tried was turning the MagSafe end part around. What i mean is: you know the part at the end of the cable that hooks into your computer? Well flip it around and then connect it. So say you connect the Magsafe to the port and the wire is outward [away from your mac]
well flip that around so the wire runs next to the other ports.
if that doesn't make sense ill make a drawing or something.
These are extremely weird solutions, but well they worked for my sister. Interesting world we live in lol..
if this fails, just make an appointment at the Genius Bar or something
GL