Water dispenser continues to leak

Our GE Artica refrigerator water dispenser just started leaking water as if a cup was pressed against the lever. Luckily I was in the kitchen when it happened so that I could shut the water line off. I noticed that the light also stayed on in the dispenser even if I pushed the light button. I then pushed the crushed ice and it started spewing crush ice until I selected the water. Since the valve was shutoff, no additional water flowed.

I then unplugged the refrigerator for 5 minutes. When I turned the refrigerator back on, the light was off. When I selected the ice or crushed ice nothing happened. I was now able to control turning the light on and off. It appears now that the water, crushed ice and cubes buttons are not working when I put a cup against the lever.

Any ideas as to what may have failed? The refrigerator is 10 years old.