Hi Rego, I am having a very similar problem. It seems like one of the wires developed a short from opening and closing the door. My early warning signs was when it started tripping the GFI every time we opened the door.
A month or two later and the dispenser stopped working and the ice maker wasn't making any ice. While troubleshooting, I noticed that the green light on the ice maker would turn on or off depending on the position that I held the door in. Of course when it gets near the closed position, it is off.
I spent a couple days last week searching for the wire harness that connects under the hinge cover and feeds into the door, but could not find it. I started disassembling the door this weekend thinking that maybe I could separate the inner plastic shell from the door so that I could get at the wires and just bypass the broken wire, but that proved to be a dead end. It appears that even with all of the screws out, the inner shell does not separate from the door. I thought maybe if I remove the door gasket that it may reveal more screws, but decided against it since doing so may have damaged the gasket.
I may try drilling and fishing wires to see if I can manage a cheap fix (it's my fridge), because from what I can tell a new door is going to set me back about $500 and may not match the other door.
Did you end up going that route or did you try fishing some wires?