I just googled the solenoid... to make sure I'm testing the right part. The pictures all look like the one that I'm testing- so it's the solenoid that is clicking. (just adding that cause I have absolutely no idea what I'm doing- I'm sure you already knew that though lol)

 

Unless I missed part of the thread you don't really specify the make of the bike. On the 110 TaoTao the starter drives a chain to turn the engine over. If it is the same set up then it sounds more like the chain is jammed or worst case scenerio there is more damage than you think. Don't want to alarm you but there is that possiblity. You say the starter clicks and jumps. the starter should be solid to the engine which makes me think the starter is loose and could twist the chain enough to bind the starter. Hard to diagnois without a visual. Hopefully someone else with more experiance on these little bikes can help.

 

Your 12.53V at the battery, and 12.05V when the solenoid is clicked in is important info. It points away from the battery being the culprit. But equally important is ths voltage at your starter motor while attempting to start the quad. You need to this exactly and report your results:

Place the red lead from the meter (20 volt DC scale) on the big red wire going into the starter motor. Place the black meter lead right on the starter motor case. You may have to dig in the probes to get good connection. Measure this voltage while attempting to crank the starter. What do you measure here?

If you have good voltage at the battery, and really low voltage at the starter motor then the power wiring connections, the solenoid itself, or the ground return wiring is bad. Then we concentrate further there. On the other hand, if you have good voltage right at the starter motor, then your starter is bad.

 

Ok I tested where the wire from the solenoid goes into the bottom of the engine. When start button was pressed it read 11.97.

 

In an earlier post you said the starter clicks and jumps. Could you possibly explain the "jump" part a bit more? Does it actually move or is it more like a shudder where it feels lke it moves but doesn't really? I would think that 11.97 volts would at least roll the engine over. Lynn can explain things that way better but just a thought, could she not maybe have a bad cell giving a good voltage reading but not the amps needed? I get confused on that regard.

 

Do you mean the starter or the solenoid. I had a similar problem on my farm quad the solenoid clicked but didnot make a connection. Have you tried a jump lead from the battery straight to the starter motor. ensure ignition is on and you are in neutral. that will identify if its the solonoid. Another way would be to do it with the multimeter to see if there is power being sent to the starter motor as indicated previous.

 

Get a new starter should fix your problem.

 

You've got 11.97 volts at the starter motor input post measured relative to the starter motor case/frame. That is more than enough voltage to crank the starter, so he starter must be bad.

Let's consider another possibility: The engine is too hard to turn, and the starter cannot turn the frozen engine. Your voltage measurement at the starter of 11.97 volts rules that possibility out too. A frozen engine would stall a good starter, but a good starter motor would draw a lot more current than the normal 30 amps, and would draw down the battery voltage much lower that just to 11.97 volts.

If all the measurement voltages you reported are correct then you have a bad starter motor.

 

Well at least your having a go which is more than some would.
Is it hard to take the starter motor off and see if it still spins when you press the button. That way you will determine if you have a locked engine.

 

I don't know the price of a starter in your area but up here in the not so frozen ,yet, north , they are fairly cheap. Don't know your budget so the cheapest method to test the starter is as mentioned, remove it to test. If you go that route once the starter is removed you need to ground the starter. Run your black jumper cable to the body of the starter and other end to the neg post on the battery. Attatch the red end to the positive terminal of the battery and touch the other end to the starter terminal.If it spins over ,you might have deeper seated problems. If it doesn't then the starter is done. the starter is a wearable unit and not surprising if it is bad. Had them go bad on just about any make of equipment ,cars trucks bikes etc that Ive owned.