Fluk, based on my experience with these refrigerators, I'd bet you the Mother Board has failed. That's where the clicking is coming from. To verify this, pull the refrigerator out away from the wall then remove the aluminum panel back there (there are 4 screws holding it in place). This will expose the mother board. You won't have to use any more tools to diagnose it... you'll hear the clicking sound coming from this board.
Your 5 yr. warranty information only applies to the sealed system components; compressor, condenser, evaporator and freon. The board isn't covered, I'm sorry to say. You can try calling GE at 1-800-GE-CARES (1-800-432-2737) and explain to them that your board has failed, but I doubt you'd get very far. (They will probably try to talk you into having a GE repair company come out and do the repair, though. <-- at a cost of about $275.00.)
You can repair this for the cost of the part... about $120.00. The part number you'll need is WR55X10552 and can be obtained from your local appliance parts store (like Sears) or purchased online
. There is an instruction sheet that comes with the replacement part... read it carefully. This is a very easy repair, it can be done in about 20 minutes. Remember... If you repair it yourself, UNPLUG YOUR FRIDGE BEFORE YOU BEGIN!!!
*TIP---> After you have the repair completed, plug your fridge into a quality surge protector, like this one
or something similar.