I can't burn the bootloader.
Is five volts present at the 5V pin?Is 3.3 volts present at the 3.3V pin?
You have to have a programmer or another Arduino board acting as a programmer to burn a bootloader.For what you've described, the board itself is OK but the processor has either lost the bootloader or has been damaged. The next step is to get a replacement processor with a bootloader already installed.
Except getting another board!
Another board isn't the end of the world. I regularly use two boards, eg. to send from one to the other.Also if you have a second board you can set it up to program the bootloader on the first board, once you get the replacement chip. From the sound of it you zapped the processor with your 12V.
The replacement chips are only about $5 so you have probably only wasted that.