You should check your power adapter/power brick whether its working nicely or not ?
For that i advice you to connect your Mac to your friend’s Mac’s power adapter. If this will not solve the issue then, you need to contact apple tech support. May be replacing that connector will fix the issue. And if connecting your Mac with your friend’s Mac’s power adapter solves the issue then, you need to connect your Mac’s power adapter to your friends Mac. Now if you find that your friend’s Mac starts behaving crazy then, you simply need to replace your power adapter…Not completely sure but may be this could be the solution.
Hope this helps a bit…
Cheers 