I've gotten to the "put in the batteries and test to see if the LED is blinking" step and my LED isn't blinking. My battery pack is testing @ 3.2V. The connection from the battery pack, at the board, is testing @3.2V. The switch tests @ 0V, but reads in the 2.92V-2.96V range, but I only depressed the button about a dozen times. The highest was 3.01V and the lowest was 2.87V.
I've examined my soldering, and everything appears to be good. In the photos, you can see some schmutz at the LED--carmelized PCB from resoldering the battery wires. I cannot see a bridge at the LED or between the LED and battery. And I'm not measuring any continuity between LED leads or LED and power
The o^ in the IC is on the slotted end, and the slotted end faces the LED end. If I recall from troubleshooting, that should indicate that the IC is properly aligned, and the LED not firing isn't a result of a misaligned IC.
So...with battery output good, power input to the board good, the switch apparently working as expected, and the IC properly aligned, I'm guessing it's faulty solder or a bad LED. Does that sound like a reasonable assumption? Is there anything else I should be checking?