Refrigerator not cooling fully

You unit appears to be 12 years old and I suspect it might be at the end of it's useful life probably due to cumulative blockage of the boiler tube over the years. I would first try and check to see if it's actually cooling and probably the best way is to take and fill up the freezer with pre frozen food and put a remote reading thermometer with a high low memory in the very back against the back wall and record the high and low each day over say a 3 or 4 day period. This should give you a reasonable indication if the actual cooling system is working properly.

All the other suggestions are good, but if it can't keep ice frozen then you might have issue bigger than what has already been mentioned.

Larry