What is a salt cell?
Your chlorinator is a miniature chlorine manufacturing plant. Firstly, The action of salt water passing through the salt cell causes electrolysis which creates chlorine (Sodium Hypochlorite) that is then returned to the pool.
The easiest way to be certain if the chlorinator is working is to make sure the cell is clean by checking the needle or production lights on the chlorinator box. When operating, you should also see bubbles (hypochloride gas) inside the chamber, producing what looks like cloudy water - that's chlorine being created! If you don't have a clear housing to view chlorine being made, many salt cells can be removed from the housing and placed in a bucket of salty pool water. Turn it on and look for tiny bubbles or cloudy water being created.
Tip: Remember less salt = less chlorine. So, check your salt level first.
Also important is to clean the electrode terminals, which can develop corrosion similar to car battery terminals. Terminal corrosion can be removed with an old toothbrush dipped into an acid solution.
Check output leads and replace if required, there are also half lead kits on the market to make it an easy fix. The salt cell will eventually lose performance and the controller circuit boards can develop problems over time.