I soldered everything together today, using red LEDs and two batteries in positions 1 and 2 as per instructions. My solder points are perfect, but I went over this board dozens of times looking for shorts and I can't find a single one. I even gave it to an electronics expert, and he looked it over for 30 minutes and couldn't find anything obviously wrong with it.
When I plug both batteries in, I get the normal LED initialization, then the two steady LEDs, and when I hit the button and wave a magnet across the sensor, I get flashing LEDs and everything works perfectly. Except that after about 30 seconds, one of the batteries starts to get extremely hot. Hot enough that it burns my fingers. It's the battery that's right next to the programming header on the left.
Here's a photo album of some shots I took of my board, but the camera I used isn't the best quality. If someone thinks it will be helpful, I can try to locate a higher quality camera and upload more pictures.
Help is much appreciated!