I ordered a new, pre-programmed chip from Adafruit. After installing it, it has the same problem. The TX and RX lights stay on, unless powered by a new 9-volt battery, and even then the board does nothing, not even running the blink program that should be installed. The reset button still does absolutely nothing, and it will not allow me to install a driver to the board.
Also, the Device Manager says that "Windows has stopped the device because it has reported problems. (Code 43)"