Thanks for the reply and the pointer to the schematic.
The reason I think the reset button doesn't work is that with a blinking LED sketch running, there is no interruption (*) in the blink. Touching the reset pin to ground resets instantly.
(*) If I mash the button enough, it resets so I suppose the button is flaky or perhaps there is a cold solder joint between it and the circuit board.
Edit: I should really test all of the other inputs and outputs to make sure they work.
Edit #2: I ran a digital output sketch and all pins worked (except, of course, A6 and A7.) I did not try inputs, presuming if outputs were good, inputs would as well. Analog inputs nearly as good. All worked except A7. Using a 10K pot for the AnalogInput example sketch, it read a solid zero through the entire sweep of the pot. Checking voltage it pulls the voltage to nearly zero as well, so it must have a short somewhere.