How to fix a locked or stucked engine on a 1982 kawasaki kz 750 ?

Its probably a fuse. I had a similar issue with tach and spedo not working:

https://www.google.com/search?q=1982+Kawasaki+KZ1000+fuse+diag&biw=1920&bih=1073&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjc4_7GorLMAhVKOCYKHXRfCbEQ_AUIBygC&dpr=0.75#imgrc=YYHbwSWvI_m9FM%3A

1982 Kawasaki KZ1000 fuse diag Google Search

Likely the seals in the Pet Co ck are leaking- purchase a new one or rebuild

Follow the specific instructions in the Factory Service Manual. Step 1 - Remove the heavy wire from the starter solenoid. Either end will suffice. Step 2 - Remove the chrome cover over the starter. Step 3 - remove the screws that hold the starter motor in place. Step 4 - Lift the starter motor out of the engine. NOTE: removing the carbs may make this step simpler. The "business" end of the starter should come out of the splined starter clutch gear. If you have trouble removing the starter from the clutch gear, you may need to remove the left side stator cover to gain access to the starter clutch and chain. The exploded parts diagram is available HERE Kawasaki Motorcycle Parts 1982 KZ1000 J2 STARTER MOTOR STARTER CLUTCH...

take a plug out fit it back into the plug cap and rest it against the cylinder head(away fom the plug hole) turn the engine over and look for a spark at the plug, make sure the hexagonal part(spanner part) of the plug is touching the cylinder head. dont touch the plug while turning the engine over ,this shock will hurt.

here
http://www.servicerepairmanualonline.com/539/76-79-kawasaki-kz750-kz-750-b-twin-service-repair-workshop-manual/
it should help!

Check if there's any play within the bearings..top and bottom of the triple tree. Put your bike on the center stand and ask someone to sit onthe bike seat and tht way it will raise in the front, try to shake the triple tree into forward and backward motion, if you do find some play thn try to adjust them(bearing)...careful not to keep em tight or else you wont get a good balance on the steering whiles riding!
Check the bushing at the handle bar too!
Hope this helps!

www.kzrider.com
great site for these kz bikes ,,