Burnt MagSafe pin, not charging

Hi,

I have an early 2011 15' MBP with the original charger. It was working fine until it suddenly stopped charging. I tried different outlets and rotating the magsafe connector but there was no LED or charging.

I saw the connection between the MagSafe an the MBP and there was a burn pin that didn't go back to the original position. Also, the same place was burnt on the socket side. Now the mac will not charge at all.

Here are some pictures:



I have a few questions:
What could have caused the faliure? The cable was a bit frayed and fixed with tape.
Is it possible that the faliure was caused by the MagSafe section inside the Mac? That means i'll have to buy a replacement and charger.
Is it safe to use a spare 60W charger instead or it will also burn? I know it will charge only when it's off. At least to make a copy of my important files to work on another computer meanwhile.

The Mac kept running after i realized so at least the logic board is not dead (phew!)

Thanks for the advice! As it's my working Mac, I need it running as soon as possible!!

I searched on ifixit and it's not soldered. I'll buy a replacement anyway and repair it just in case

And a new charger?