Has your Macbook Pro suffered a drop or a spill of any sort?
I thought as much, as it does sound like you have damaged the logic board.
If it were just the keyboard, then I would have suggested opening it up to see if there are any loose connections, which you still may want to do.
You could take it to Apple to have it looked at, but if it is the logic board, having Apple repair it would cost you more than the computer is worth, and even if you source a logic board and did it yourself, it would still amount to pretty much what your Mac is worth.