Samsung Ice maker stopped working
Mary, how much can you do yourself?  I will share my experience, but I will also preface it with the fact I have my own hand tools, as well as a multimeter for diagnosing electrical problems.  You need to be able to get to the ice maker itself, and be able to disassemble/remove it from the frig, if need be.
I fixed my ice maker within the last year, but my frig. doesn't have water, so YMMV. the troubleshooting is the same. Find the water supply line to the icemaker (it might be different from the one for water dispenser).  the water supply line in the frig. will start at a water solenoid valve that usually is connected to the water supply line of the house (coming out of the wall and w/ a shutoff valve).  easiest way to test the solenoid valve is to disconnect the water supply line (at the solenoid) to ice maker and energize the solenoid to see if it works (this is assuming there's a separate solenoid for each ice maker and water dispenser). Cycle the unit however you can, maybe unplugging and then plugging back in the frig's electrical cord.  If the solenoid for ice maker dispenses water, then the solenoid is okay, and you can move on to next troubleshooting step.  If the solenoid doesn't dispense water, then that's most likely your issue.
Second step, remove the water supply line from the ice maker. You might have to unmount the icemaker from the wall of the frig. the idea is to see that you have water running all the way to the icemaker. if you don't then you have a clog (unlikely) in your supply line between solenoid and icemaker.  You might have to energize that solenoid again to push water through that line. If you do have water there, then go to next step.
Third step: depending on how new your frig is, the icemaker's controls will be mechanical or electronic. Mechanical controls are the lesser expensive option, and so more common to find, even in newer models.  The point is a lot of times the mechanical timer for the icemaker is what craps out.  It's a lot like the timer on a washing machine. It controls the different cycles of the icemaker.  First, the icemaker fills w/ water; then the water freezes; then the bottom of the icemaker heats up to release the ice, and then a mechanical arm/auger lifts/pushes out the ice into the basket. These steps are controlled by the timer.  These timers go bad, and most people will typically replace the whole ice maker, which isn't necessary.  The timers are available and replacing the timer is a whole lot cheaper than the whole ice maker, or even the frig.  The timer is fairly easy to troubleshoot, assuming you want to make sure. this is where the multimeter comes in and cheap ones are available at harbor freight and online if you need one.  the operation of the multimeter is pretty simple and can be learned online relatively quickly on YouTube. you can even find a video that explains these steps and shows where to look and some even show how to setup the multimeter.  A faulty timer is fairly easy to replace.  You might or might not have to remove the icemaker. getting to it will be the most labor intensive part of the job. Mine is in a bottom freeze, and I removed the bottom door and racks/shelving (and all the food) to get to the icemaker.
In summary, I troubleshot and repaired my icemaker to the tune of maybe 30 or 40 dollars, as opposed to spending couple of hundred dollars just for an icemaker and even more for a professional to do it, at which point that's when people decide just to replace the whole frig.  Hope this helps.