Okay, I figured mine out. I removed the circuit board from the bezel (8 or 9 screws on the circuit board itself) and found the IR sensor on the front of the circuit board. I then looked on the back of the circuit board at the corresponding location, and sure enough, I found three joints in a row, and some cracked solder on two of the three joints. I've never soldered before, but called someone I know, asked the technique, and had it fixed in ten minutes. This thing had been broken for three years.
Good luck, mmoerk2.
For anyone else with a 405 or any other model different from the 507, just find your IR sensor on the front of the circuit board, and look closely at the joints on the other side of the board at that location.

Can't wait to reassemble this thing and use my remote again!!!!!!!