If the pool has high levels of chlorine and/or exposure to sunlight, the CCs can stay near zero. It all depends on the nature of the organics in the pool. Some only slowly form CCs so sunlight can break it down as fast as it is produced. Others such as ammonia from chloramines very, very quickly and will register on the tests before they get broken down.

As recommended, I would shock the pool and also brush the sides. Though maybe you don't actually have algae, odds are you've got something that needs to be broken down and more likely than not it is algae trying to form. A slimy feel is probably an algal slime layer getting formed. Either that or your pool is oozing something it's alive, it's alive!

Richard