I have recently replaced a broken solenoid sending water to the refrigerator ice maker. I replaced the part according to the instructions but the unit still is not getting any water. There is water on the line. Could it be another part triggering the solenoid to start?
check where the saddle valve connects to the main water line. Shut off the saddle valve and pull the plastic line out of it and then turn the saddle valve back on. It should shoot water forcefully. If not replace it. This valve is about $4. very easy to replace, and should solve your problem.
Does it click when you try to get water flowing? You might want to take a voltmeter to it and see if there is power going to it when the icemaker is engaged. If not then the problem lies with the icemaker itself.