I just spent 2 hours on this problem and finally found a fix.. The real solution is to replace the water filter mount because more than likely, the water inlet nipple is broken. It was mentioned in another solution so, I decided to check it out with a mirror and found out that it was crooked. I took the part out, after checking everything else, and saw that it has little wings that were supposed to keep it straight, allowing for it to be pushed to let the water flow into the filter. If it's not fixed, after the pressure builds, it slides off to the slide and closes again. So, the proper fix is to replace the mount... but I snipped off a tip of a plastic fork and used it to keep the nipple straight; re-mounted the mount; attached all the water lines I had disconnected; hooked up the new filter (GE MWF); and turned on the water... it worked!!
So, the short of it... turn off the water to the fridge. Unplug the fridge. Disconnect both water lines that go to the filter and the back, top cover where they go in from the back. Now you can take out the mount and replace it... or flip it over and find a way to fix the nipple... your choice...