Sorry I am not sure, what is going on, but my first guess would be to check any soldering, since digital pin 12 is next to a 3.3v pin, so if there is some stray solder between these two pins, then pressing the button would ground the 3.3v pin to GND, which would at best reset the board...
So with your meter I would check the resistance between pin 12 and 3.3v.
But again this is just guessing.