Hi Patti,
A couple of things could be going on here. I will assist with trouble shooting if you are up for it.
First of all, the hot rail between the freezer and fresh food sections concerns me. This is an indication that the condenser is too hot, this could be causing the compressor to overheat and you may be not cooling properly. The freezer may be cold but not cold enough to run the ice maker right. If you have ice cream in the freezer and it is hard then you are okay if the ice cream is soft then you are too warm. If you have a thermometer you can check, you need to be 5 degrees F or less for proper ice making.
See the first link at the bottom of this to repair the hot rail condition. Or let me know if need more details.
If the temperature is okay then you can test the ice maker and water valve to determine which one is the problem. On the face of the icemaker itself is a white square cover. when you pull off this cover, (it may be froze on and stuck but will pull off) you will see something similar the picture below. around the tan colored module you will see several holes with a letter by each hole. THIS NEXT STEP IS WORKING WITH ELECTRICAL POWER ON IF YOU ARE NOT COMFORTABLE WITH THIS DO NOT ATTEMPT. Using an insulated wire so you do not get a shock, put a wire connecting holes L to V you will be testing the water valve. If you hear the valve buzzing and water comes out then the valve is good, if you hear the valve buzz and no water then the water line is frozen between the valve and ice maker, if you hear no buzz at all then the valve is bad. The valve is located behind the frig in the bottom right corner looking from the back.
I am strongly suspecting your problem to be with the hot condenser more than anything else.
Let me know if you need more details or information
Hot Rail