There is a water valve under the fridge that needs replaced.
Be good place to start. When is the last time the filter was changed?
See if you can isolate the tube supplying the water dispenser. Remove it and put a piece of tubing on it and place the tube in a bucket. Press the dispenser control and see if it puts water in the bucket. If it does, you may have a filter problem.
There are other ways to check the inlet valve, but this is the safest.
Note: This is not a fool-proof test. If the micro switch for the dispenser is bad, the valve will not dispense water into the bucket even if the valve is good.
The valve itself can be tested for continuity or checked with a live wire. Checking with a live wire is not the safest way!
All that being said, it has been a while since I have done app repair, and this fridge may not have a micro switch for the dispenser. The newer ones may be connected straight to an electronic control board.
I will say this, most of the time this kind of problem was a simple fix.