Safe to assume the hour hand is not running either given that it is ultimately driven by the canon pinion->minute Wheel->hour wheel. In addition to the keyless work, this could be a basic issue with the motion work. Could be a broken tooth on the canon pinion, minute wheel or hour wheel. Could simply be a loose canon pinion. When setting the hands, do they move extremely freely -- i.e. too loose, or can you feel some resistance caused by the friction fit of the canon pinion to the center wheel post??? What lubrication did you use on the post prior to installing the canon pinion? Are you 100% certain that the canon pinion is set fully onto the post?
Removing the dial is critical. Perhaps your keyless work is not installed correctly (e.g. yoke or yoke spring) and the sliding pinion (clutch) is engaging the intermediate wheel when it should not be - this would stop the minute and hour hands, but not the second hand.
Good luck!