I have a KYMCO 4 wheeler that will not start...Checked starter solenoid and found only 10 volts being supplied to it, yet 12 volt battery is fully charged

10 volts means that it is a dead battery
have a load test done on the battery
have the charging system checked by an accredited auto electrician
battery voltage should be 12 volts at all times with it rising to 14.5-14.8 volts dc at 2000rpm

A clicking starter solenoid is usually caused by a discharged or defective battery. I would charge the battery and check the connections. The battery voltage should remain above 10 volts WHILE CRANKING.

does it crank at all , if not then ck and make sure you battery is good , do you have a bad wire, if your wire is long you will always lose volts which is normal , but does it crank over , if not then try jump starting it with a car or something unless you have a good battery charger which will work just as well ,are you getting voltage when you crank it from the other side of the solenoid if not you have a bad solenoid , has to crank or it will never start ,

Check battery must fully charged, check starter fuse and relay Check 12 volt wire from ignition switch to starter relay in the fuse box ,then check 12 volt wire from starter relay to starter motor solenoid if if it's everything is ok then change the starter.

Buy you a $10 volt ohm meter. Set it on DC Volts 20 volt scale or that range. Find starter solenoid place leads on small wire connectors have someone try and crank when they do you should have 12 V. If you do have the voltage you may have bad solenoid contacts. Place meter test leads on large wire contacts if you have 12 v there when the person tries to start you have open contacts on solenoid. If you do not have 12 volts on meter when person tries to start place one lead on one of the large wire post and the other on neg. Terminal on battery if you now get 12 v you probably have a bad starter.

Hi,
Sounds like a bad starter relay. When you turn your key to start, current flows through a relay which in turns supplies 12 volts to the solenoid on your starter motor. As you alluded to , typically the common clicking sound that we all hear occasionally, is usually related to a flat battery or bad starter motor, but as you have had these checked (by a professional?) the only possibility is the relay that supplies 12 volts DC to your starter motor solenoid.
Thought you might find this interesting to help you understand ignition systems:
http://auto.howstuffworks.com/ignition-system.htm
Cheers,
Steve (Melbourne, Australia)

kymco 500 has no air temp sensor,ecu reads water temp for coldstart enrickment.a new sender wont fix it ether,sender needs to read 10 degrees warmer to start

When its hooked up, you should be able to put 12 volts on the little stud on the solenoid and it should start. One large stud will have 12 volts on it, so just jump it right there. Did you get the wires in the right place. The solenoid should have 1 large wire going down to the starter. Be sure the battery cables are clean and tight ( both ends) Check battery voltage when cranking, should go to 10-11 volts. Check voltage between negative terminal on battery and engine, should be ZERO when cranking. The solenoid has 2 large studs, make sure the battery positive wire and all the other wires are hooked to this stud, the other large stud should just have the wire going to the starter.