If you've truly damaged the chip, then the ways it could be damaged are ... very many.
You're probably talking upward of 100,000 transistors for the entire chip.
"avrdude: Yikes! Invalid device signature.
Turning on "verbose" mode for upload (in preferences) will give more details.
Usually a signature of 0 or -1 means misconnections or no clocking (but it's hard to tell which, and it could be other things as well. A three-digit value of non-0/-1 would mean corruption of ROM/Flash areas that aren't supposed to be user-writeable.)
You CAN do analysis to get a better idea of what happened, but ... usually a board has to cost a lot more than $50 before this becomes economically worthwhile.