My first guess would be the solenoid where you hook the water up. They usually have a plastic housing and, would probably not drain completely. If not, check hoses that run from the valve to icemaker, They will probably run up the back, or just inside the back. It's also posible that the solenoid broke or is stuck open and could be overfilling ice tray.
http://www.partselect.com/PartDetail.aspx?Inventory=1991254&SourceCode=5&ModelNum=FRS26R4AThere filter canister may have broken also;
Filter housing froze up and burst
I had to replace this unit after a repair by the local appliance repairman. The thermostat/ damper control failed and the refrigerator section of a side by side froze up.
As far as installing this unit it goes as follows.
1.) You may want to turn off the water supply to the unit just as a safety.
2.) Remove the two screws holding the unit to the back of the refrigerator.
3.) Disconnect the two lines noting which one goes where. A simple pulling of the hose connection sleeve ( pull toward the hose ) will release the hose's
4.) Reverse the process and turn the water back on. Check for any leaks and re-attach to the back wall.