Personally I don't "repair" Quartz watches, except occational battery changes...
From what I understand most watchmakers tend to replace quarts movement instead of repairing......
I have however, for personal reasons, fiddled with some junk movements and have been very sucessful in getting "dead" movements to tick again.
This is of course not recommendable for customer movements but can function as a test.
1 - Remove the battery.
2 - Look close (loupe) and locate one or more wheels. Push on the wheels with a toothpick with the intention to turn the small magnet inside the movement.
3 - Replace the battery and keep fingers crossed!
This has worked on about 50% of the quartz movements I have tried it on. It is of course not a permanent repair but at least it tells you that the movement as such is working. I believe there is some debree stuck to the magnet (very strong) and by rotating it such debree might be pushed to the side, allowing the magnet to turn.
I have a close friend who has another trick. He puts the movement in his demagnetizer. Haven't tried it myself but it may be worth a try.
For a lasting repair a replacement movement is usually the only reliable way.
Very near the top of my list of advice is to take static precautions when you open up a quartz. You had better believe it can amount to 1000's of volts and will damage the silicon chip crystal. Yes, yes, I know they will say it has static protection. You believe in it if you want to....!
The Japanese Miyota range is cheap enough and wonderful value. Well made and lots of metal parts unlike some plastic Chinese examples which nonetheless will work for a while.
I've heard of people having some success with flushing the Miyota type movement with lighter fuel. It leaves a very fine oily residue which could be just what you don't want to attract new dust particles. However, it may flush more out than it attracts in the short term and get you going again.
If there's a chance of recovery I put them on test with a second hand to see if they are maintaining for a day or three. Any thoughts of oil should be silicone thoughts if this is a clock with plastic wheels and pinions.
There are some other things to check. The battery contacts under a glass - even the gold plated types can oxidise or corrode. It will need to be cleaned off and any gold will go with it. The part can sometimes be replaced. Old movements can be a useful source. I have some very old contact cleaner gel. The tiniest amount on the battery terminal might prevent a repeat. Old batteries and a damp atmosphere probably precipitate the corrosion process?
Test the new battery can maintain its voltage under load. The normal drain is 1 to 2uA for a 3 hand + date types. (wrist-watch). If you ask it to deliver just fleetingly 10mA at 1.5V - then you'll need a 150R resistor. (Say for 2 seconds is long enough). The voltage should remain above 1.5V and stable. No drooping. Try to appreciate the difference between the various button cell technologies. The life (energy reserve) they have and the subtle difference in voltage. The quality behind the maker etc. etc.
Next make sure the hands are passing each other and the dial hasn't slipped to foul the cannon. Some movements switch off the motor when the crown is pulled out and this means there is a switch in there. A few operations will probably clean it if you're the lucky sort.
You CAN measure the coil - which is so easily damaged by a careless battery change - with an ohm-meter BUT it will apply a small voltage to the electronics and that is not best practice.
It will measure about 1000 to 2000 ohms
You will do better checking the drive first with an oscilloscope although some say you can see pulses with a high resistance voltmeter. The pulse is narrow and at 1 second intervals to step the motor. It reverses polarity on each beat. Therefore you will need an old fashioned analogue meter with a pointer and it will dip below the zero mark for negative. About a volt or so. Some such meters have a zero adjuster for the pointer. You can make temporary use of that to help.
On a scope with reasonable trace retention you'll see the waveform. Many will let you capture the display. I'll post some pictures - the best I could get. It shows two waveforms - Blue & Yellow. You can choose either. The polarity is swapped by a "H bridge" which is all part of the electronic circuit. So the pulses alternately rise above zero then fall beneath zero (-ve). The motor turns a half rev with each pulse of resulting magnetic flux which is swapping its North & South poles to make it happen.
Lastly - the quartz crystal. Usually 32Khz they can fail. You can buy new ones. Its soldered in place. Good luck with that....! Heat here will damage everything. Be super quick. Use a little liquid flux. Wash it off afterwards with some Isopropyl on a small make-up brush.
I have dismantled a few movements. Its tricky - not really worth the candle unless you're made that way.
I hope this helps. Best rgds, BerryG
'Bug ... There's usually a thin plastic film insulator underneath the battery which some folks don't notice during a battery change. If that has been, or gets, damaged or inadvertently removed the movement won't work.
I successfully replaced the quartz movement in a 1970s Majesti pocket watch (had a Harley Ronda 313 in it, and I put in a 713 'cause the 313 was discontinued and no longer available) a few weeks ago. The hardest part was getting the hands back on, especially the second hand. I toyed with the idea of just replacing the coil, which seemed to be the usual culprit, but the movement was so cheap that it didn't seem worth the gamble to save a few bucks.
The coil needs to be removed from the watch for testing. Never waste your time and the watch by attempting to test it in the watch.
I've serviced thousands of quartz watches. Even repaired the broken coils, if I have to.