how can I tell if my auto chlorinator is working???

how do I test the functionality of the automatic chlorinator?? I put 4 chlorine tabs in it on Sunday..Today it seems like they are still in there, almost completely in tact and the dial is turned all the way up to 5. My pool is still a green swamp today. Of course we got some more rain today too...will my pool ever come back to life? I also re-shocked it today..thats 3 times this week. Thanks for all the help for this newbie..