Knocker - does the knocker work in the coil test mode?
Kickback - disassemble and look for mechanical issues (mushroomed plunger, bad coil sleeve, etc.) if the coil sleeve isn't easily removed from the coil, the coil may be swollen and need replacement. Replacing the coil usually isn't needed.
Slingshot - put your meter on VDC and measure between the coil and ground, should see 50+ volts on both sides of the coil. If it's getting voltage, something's up with the control circuitry or wiring on the control line.