If you are not connecting a Programmer to the 2x3 ICSP header on the board, then selecting AVR MKii or anything else will not make a difference.
More than likely, some static electricity from dry winters homes is zapping the USB/Serial chip, or the 328P chip, or there is no bootloader installed, or the bootloader has become corrupted.
Feel the chip when it is powered up. Is it hot to the touch? That is another indication that something fried the chip.
The bootloader is the Programmer referred to in the "programmer is not responding" message - the 328P is not talking to the PC.
You could get a Programmer, like this one, and see if the bootloader on the non-working boards can be restored.
Also, measure the 3.3V and 5V on the power header, see it the board has good power.
