This can be a little tricky to pull off if you've never done it before. Find a thin putty knife or small screwdriver insert about 1/2 inch from the side of the unit underneath the control panel there is a metal clip on either side you may need to (once located) smack the handle of your tool to dislodge the clips. You can get a better view of you need by removing the back panel of the control. Once the control is off remove the screws holding down the top (2-4 Philips) then pull front then lift up. Hope this helps good luck!
The technicians should be able to find a leak if there is one. They should reclaim the refrigerant within the unit. Then vacuum down the sealed system. Recharge the system with nitrogen or use a dye. Then fix the leak or Replace the component. Evaporator coil, condenser coil, compressor, etc.
Depending on your model number, you may be able to self cycle your ice maker. If you are able do so make sure your spout to your ice maker is clear of ice and give it a try. Your issue is most likey your ice maker itself or the water solenoid valve.