Then I remember Flylady! This is how she recommends we clean our sinks:
Make sure you rinse well in between each step!
1.) Take all the dishes out of the sink.
2.) Run some very hot water into the sink. Fill to the rim. Only do one side at a time. Then, pour a cup of household bleach into the hot water. Let it sit for 1 hour. Now, pull the plug with a pair of tongs. If you don't have tongs, then scoop some of the water out of the sink into the other sink and use your hand to pull the plug (wear gloves and don't get the bleach-water on your clothes).
3.) Rinse your sink well.
4.) Use some cleanser (Comet, Ajax, or Baking Soda) and scrub your sink. Ensure you rinse ALL of the cleanser from the sink.
5.) Take a sharp edge and clean around the rim of the sink, just like you would clean dirt out from under your fingernails.
6.) Clean around the faucets too. You may need an old toothbrush or dental floss.
7.) Now, get out your window cleaner, I use Windex, and give it a good shine.
8.) If you still don't like the way it looks, then you could try some car wax. Just know in your heart that you have cleaned it very well now and it doesn't have to be perfect. Our perfectionism is what got us in this situation in the first place.
*Flylady goes on to encourage us to wipe out the sink with a clean cloth each time it is used. I don't do this because I don't want to go crazy when someone else doesn't do it! hehe!
Now I LOVE my sink!