OP

Quoted from pbain:

Problem solved. Thank you Howard for all your help and encouragement. I couldn't have done it without you.
(I wish there was good video tutorial on reading a schematic.)
The switches on the AX and BX relays needed adjustment. That was huge.
Then I checked the board for shorts (checking all wires and lamps). I found one frayed wire and fixed it.
The machine was blowing a fuse now. After going through 6 fuses, I built a circuit breaker fuse like the one here http://www.pinrepair.com/em/index1.htm#top
(Unfortunately, we don't have Radio Shack anymore and none of the hardware stores had anything below a 15 AMP breaker. I found a 10 AMP breker at a marine supply store.)
Remembering the coils I replaced and how the pop bumper coils had diodes, I checked the coil for the chime box. Sure enough, tucked away in there was a diode. I cut and removed the diode from the coil and all worked!
I'm not sure why the coil shipped with a diode on it, but it did. So the lesson learned is: CUT THE DIODE on the coil if you are replacing a coil without a diode!