Mid-2012 MacBook Pro won't charge with stock L-tip, works with T-tip

I have a mid 2012 MBP with an i7 and GTX 650M. It came with an 85W L-tipped magsafe AC adapter. It now no longer makes a connection in any way, the LED on the adapter doesn't light up, and the MBP doesn't respond to being plugged in at all. I tried the AC adapter on other Macs, and it works as it should. I then happened to try the 85W T-tipped magsafe off my girlfriend's older C2D Mac, and it works, but you have to move it around to make a connection. I've tried resetting the SMC, but it doesn't seem to change anything. I'm not even sure I've done it correctly as there is no onscreen confirmation or anything that would indicate a change. I've tried updating the firmware directly but it tells me I don't need it. What does this indicate to you? Do you think it is merely the port on the MBP? I opened it up and it doesn't seem hard to change. There is even an ebay listing for just this, which I am certain I could do myself, but I might as well spend a few more bucks and get the whole unit. The Magsafe daughterboard is marked 820-2565-A, and a search seems to indicate that the same board is found in many other MBs, some of which may not be the same wattage? Does that matter? Or are they the same?

Cheers,

Alex