I have doorbell near my garage door and a doorbell at my front door. Both doorbells run through the same transformer to the chime. The garage door button activates the chime. However, the front door button does not activate its chime.
I have a light in the front door bell button and the light works. If I disconnect the door bell button from its two wires, and touch the two wires together I get a spark. So, I know I have power at the front door bell button.
When the garage door button is activated its plunger moves against the chime. When the front door button is activated its plunger does not move. Where do you think my problem lies?

Try going to the chime unit and switch the front and rear wires. It the Rear button now works, the rear chime is shorted or binding, see if you can physically move both plungers.

Thanks, I will give that a shot.

Strats got the technique to trouble shooting. You can usually clean up the plungers by lightly rubbing them with WD 40 and 0000 steel wool. Use a rag to dry them off and they should work.