UPDATE 3
I replaced the water filter with a brand new one from Home Depot. When I went to dispense water, about 1/2 a cup came out. That's the first time any water has come out of the dispenser. Over the next hour, I tried dispensing more water. One time a blast of water came out, but every other time I would just hear water bubbling and gurgling in the freezer door. I thought maybe things just needed to fill up since it hadn't been used in a while, but now it's back to how it was before I got the new filter. I press the button to dispense water, and I hear a 'click' and a motorized sound, but no water dispenses.
Could my lines be clogged?
UPDATE 2
I forgot to mention that I've thought it was weird that this guy was sticking out and was so visible. It looks like it's a water supply line that goes up the freezer door, on the left. Could the plumber have tweaked this?
UPDATE
With the help of Jimmy-Fix-It, I was able to get the water filter removed after applying considerable force. Water dribbled out, and it was, as expected, filled with water.
After I removed the filter, I took a cup and tried to get water out of door, and about 1 Tbs came out. No water has come out since.
We just moved in to a new home. The former owner was in the field of risk management/disaster cleanup, and so when they put the house up for sale, they disabled the refrigerator's ability to make ice and serve water. We didn't realize this of course until after we moved in. I spoke with him on the phone, and he told me he had his plumber essentially disable the ice making/water serving abilities of the fridge. He was supposed to send his plumber out to turn it back on, but he's stopped returning my emails.
I've pulled the fridge (an LG LSC26905) out from the wall. The water line is connected just fine to the refrigerator, and I've confirmed that the water is in fact on (coming from the wall). It's a simple silver flex tube coming from the wall with a blue valve that is in the 'on' position. I disconnected from the fridge and verified that water is coming out at a very good rate. I can't figure out where the plumber might have disabled or prevented the water from flowing through the rest of the system.
The only other thing I've noticed, and I'm not sure it's related, is that the water filter will not come out. It looks to be pretty old, and for the life of me I can not pull it out. I'm wondering if perhaps the filter is old and clogged and that's preventing water from flowing through the system? I've twisted both directions, pushed up, pulled down; it's not budging.
Best Answer
So turns out the water valve in the back of my fridge was bad. All rusted out. I broke down and called a technician (thankfully) and he said we were lucky it didn't burst, as it probably would have flooded the house. On top of that, the condenser fan motor was dead.
I suspect the former owner knew all of this, and just had his guy go behind the fridge and shut off the main water line to the fridge so they wouldn't have to deal with it before selling the house.