If that red light is next to a rocker off and on switch the ice maker is bad and needs replaced. That sounds like a GE ice maker and the light should be green like the one in the picture below.
Of course you can. The replacement is very simple. Remove the old one and put in the new one. Switch it on and in about an hour it starts making ice. If you could provide the model number I will get you the correct part number.
I am sorry for the delayed reply. I just got in from work.
Ah that shines a lot of light. That one is built by whirlpool.
When you first open the door the status led should remain solid red. If its not stop there and let me know.
Press the flapper and it should blink twice. If it does that the ice maker could be faulty.
If it does something different stop there and let me know.
First is to note the position of the ice maker fingers and if there is undumped ice in the tray of the ice maker.
On the bottom of the ice maker is one screw 1/4 inch is the size. Remove that screw and give a little tug. This will lead you to the small lock that holds the ice maker in position. Once you get that unlocked it will slide out. In the picture below is the face plate. Remove that. I know its not exact but it comes off just as pictured.
Strip a small piece of insulated wire an put the ends into the holes marked T and H as pictured below.
Tape the door switch and the emitter flap closed just like they would be if the freezer door was shut and in a minute the ice maker should begin to cycle. If it does cycle let it turn about a quarter of the way around and remove the wire. It should then continue on its own. If it cycles all the way around watch to see if water comes out of the fill tube. It should make one complete cycle and then stop.
Let me know what you find. I will be home tonight at the same time I was last night.
If everything went as described. The sequence of 2 blinks and solid as described above you only need a module. One place you can order it online is Midwayparts.net. But it is a very common replacement part and you should be able to find one locally. The part number is XXXXX
Let me give you a tip about replacing this piece. Remove the 3 screws and remove the old module. Then unlock the wiring harness from the ice maker and remove it. Install the new module with the 3 screws and then connect the harness.
Sometimes what happens is if you do not remove the harness and then install the module the connectors on the harness get bent and do not make a good connection.
Personally the pay is not why I spend some time on this site. I do appreciate it, what I really appreciate is that I know someone who was looking for help got it and I was involved. Thats what I really like. I hope I helped you, and you are most certainly welcome.