Thank you for reviewing and responding. I have called the toll free number and will, hopefully, be speaking to someone from Ring later today.
Just for clarity, I have attempted to use the reset button with no success. Both with the battery door closed and open.
Also of note, when I put a battery in either of the open slots, a red light illuminates next to the battery. When I press and hold the reset button, the light turns off. When I release the button, the red light returns. At no point does the external status light on the bottom of the device begin flashing.
This whole thing makes me wonder if there is some sort of firmware problem that is not allowing the device to recognize the presence of a battery.