Checked coil sleeve and it seems okay ? Well is it the right one, dirty, cracked on the end ? That could add to the problem.
Usually not a coil problem. Wires are solered on. If you know nothing of soldering. Learn. Google, YouTube, etc. Get an iron, solder, and wire. Sit at a table and practice. Learn to heat the wire then flow the solder so you make a good joint. If it looks like a garlic wedge, then you made a lousy cold solder joint. Taking the wires of is easy, heat them up. Anytime you work on things like this, take pictures or notes and get wires back in the right spots. In case diodes are involved you'll save yourself a lot of grief.
And the part of the mechanism that kicks the ball, is kind of peened together, check that if it's loose or any worn or broken parts on the mechanism.
LTG