Ok, problem solved. I had the push button wired up like the diagram from the picture in my previous post. The junction between HOT, GND, and digital pin 4 needed to be AFTER the resistor, not before. In other words, HOT had to pass the through the resistor before it went to the pin OR out to ground, when the button was pushed.
I should have thought of that before, since the reset button on the board operates the same way, but it taught me something at least. Thanks for the help.