Q: Problem charging macbook pro

I tried all of that before I came on here.  I should probably add some more info.  Earlier yesterday I went to an apple-certified store to get a new battery, and to test if my adapter needed to be replaced because it wouldn't power the laptop.  They tested one of their cords and it would not work, but when mine was plugged in it started working (in retrospect when I was holding the computer maybe it was tilted?).  So it's not the adapter.  Earlier today when I charged the laptop, I had to do it upside down. 

There clearly seems to be something wrong with the magsafe port.  I'm wondering if maybe there's something I could do to fix it?  Or is this maybe a sign that I'm going to have to get the port replaced?  The port is clean and there's no debris, I really don't know why it needs to be upside down or tilted to be charged. 

Also the reason why I'm asking online is because the nearest apple-certified store is about 1 1/2 hours away, so if I can resolve this without making a trip there that'd be greatly appreciated.