Hi, and welcome to the forum!!

Generally if you have that much algae on the bottom of the pool, the water won't be clear. Do you also see algae on the sides, or just the bottom? Does the liner feel slimy to you? If you reach down, can you pinch some of the "algae" up? And if you do that and rub it on a piece of paper towel, does the smear appear to be green? When you brush the pool, does the water take on a greenish tint?

How are you testing the water? If you're testing with strips, or relying on the pool store, you're probably not getting accurate results. I would highly recommend that you get the K-2006 test kit linked in my sig, but in the meantime go to WalMart and see if they have the hth 6-way kit that sells for around $20. If not, at LEAST pick up the cheap OTO kit (uses red and yellow drops).

What method do you use to chlorinate your pool, and can you give us a list of every chemical you've put into the pool during your battle with the "algae". (We need ingredients, not just "shock".). With the answers to these questions, we can give you some more helpful advice--but first we need enough info to help you isolate the problem.