Quartz watches are powered by an electronic oscillator along with a small quartz crystal. The watch's movements and inner workings include a coil that loops current through the timepiece. If the coil is damaged from being dropped or jarred, the watch will no longer keep time. Once you have removed the back of the watch and taken out the coil, you can repair it with just a few tools. You should have some experience using a soldering gun to attempt this project.
Turn on a multimeter and zero it out by touching the black and red probes together. This will render a volt reading of less than .20 volts for accurate testing to find the break in the coil.
Touch the black and red probes to the quartz watch coil in various places until you find the break. Your multimeter will either sound an alarm when you find the break or light up.
Retest the coil once you locate the break to ensure it is the only one and you are sure where the break is located.
Melt flux with a soldering gun onto the break, closing the opening in the coil. Let the flux dry for 45 to 60 seconds. Wipe away excess immediately with a rag.
Test the coil once more with the multimeter to ensure the break in the coil has been closed/fused together, then reassemble your watch and use it as normal.