I had a similar problem with my Kenmore Elite with bottom mounted freezer that turned out to be a frozen water line and/or frozen water reservoir. The short story is that I turned up the temperature in the fridge 3 degrees and the water started running the next day. The following is probably more info than you need, but here is what I did (the long story). We had a busy day with the fridge door opened and closed quite a bit so I had set the controls to Rapid Cool like the instructions said to do under those circumstances. The next day we found the water wasn't working and it didn't appear that the ice maker had made ice for a while. I suspected the water line may have frozen, but worried that the water valve may have failed. I turned up the refrigerator temperature setpoint 3 degrees F to 41 F and overnight the water was running again. That confirmed that it wasn't a bad water valve. I then turned the temperature back down to the recommended 38 F setpoint and put a digital thermometer in the refrigerator. I found that the top shelf was getting down to 32.8 F. Assuming there is some error in the thermometer I could see how the water line could freeze up. I set the refrigerator temperature setpoint to 39 F and have continued to monitor the temperature with the digital thermometer. It is holding at about 33.3 F and the water line has not frozen. It appears on my Kenmore that the refrigerator cooling comes in at the top, back of the refrigerator. So I assume the top shelf will be the coldest, but I want to check the temperature in different parts of the refrigerator to be sure. The recommended temperature for fresh food storage is 40 F so I think I can raise mine a bit and still be safe, plus avoid unnecessary energy usage keeping it too cold.
It's free to try raising the temperature to see if the lines are frozen. If that doesn't do it then it's probably a bad water valve.
Good luck,
Jim | 
