Cloudy water, but blue

My pump quit on me and I ordered a new one online. However, when it got here didn't get around to replacing it (winter in Florida so I wasn't in a big hurry) for awhile. The water turned green, and I mean GREEN. So the pump's in, I dump two 2.5gal of chlorine in and run the pump all day and all night. Next day I take the cartridge out (new) and clean it then run it some more.
The water looks great (pretty light blue) except its cloudy, can't see more than a foot down. I take a sample to Pinch-A-Penny for them to test. Says my chlorine is just fine but I need to add a whole bag of alkalinity and half a bag of stabilizer gradually to skimmer and run for three days. Just wasted $30.00 'cause the water looks the same.
Before I registered here on Poolflorum I googled my problem and came across PoolSolutions.com/100-reasons-for-cloudy-swimming-pool, low and behold there was my malady at chart topping problem number two!

Here it is:
Dead algae is still in the swimming pool pool.
If you had algae (the pool was green), but you killed it, and now the pool is cloudy blue or gray . . . dead algae may be the problem. Some types of dead algae are quite difficult to remove, especially with sand or cartridge filters.

So now what? Thanks in advance.

Have you added ANYTHING in the last 2 weeks except chlorine, stabilizer and baking soda ("alkalinity")?

If not, then you can try using a floc to settle the algae, but ONLY if you can 'vacuum to waste'. Do NOT do this if you've used other chemicals; instead, tell us what you've used. Do not do this if you can't vacuum the algae OUT of the pool.

Otherwise:

1. Get enough bleach (or liquid chlorine) to maintain your chlorine levels with the pump off.

2. Put the pump on "RECIRCULATE" if you can; otherwise, turn the pump off. Brush the pool COMPLETELY. If the pool turns green from piles of algae, add chlorine till it goes back to blue or gray.

3. Once the pool is brushed and blue. Check your chlorine. If it's more than 10 ppm, wait. Meanwhile purchase a bottle of what ever floc, your PaP store says works best for them with dead algae. Once the chlorine is below 10, add it following instructions.

4. TURN YOUR PUMP OFF, and leave it off at least 24 hours, to see if the algae will settle. Continue to add chlorine, as need to maintain adequate levels. If the algae seems to be settling wait up to 72 hours.

5. Once the algae has settled, vacuum it to waste, and the restore normal pool ops.

Update: Sorry this took so long to respond. I thought if I got any responses from my original post I would be notified via my gMail account. Well, after I posted here, I googled my problem and found a solution; clarifier. I went to Lowes, bought a bottle, followed the directions as for the amount for the volume of water in my pool and cha-ching!!! Clear water in a couple of hours running the pump! Put my little robot vacuum in and cleaned right up.

If you would, let us know what you used.

Clarifiers have undisclosed ingredients, so it's hard for us to know which ones work.