New House Old Pool

Hello Everyone,
This is my first time posting but I have been lurking for a few months now.
Here is my dilemma, I just bought a house that has been bank owned for about 3 years and it has a concrete or gunite in-ground pool but unfortunately it has been uncovered for that period of time in a lot full of trees. So the pool is green with a visibility of about 4 inches and the bottom is full of leaves and grass trimmings.
I have bought a leave rake and taken out about 15 bags full of leaves and debris but can't seem to get everything out as some of the leaves have decomposed into dirt/muck.
Should I drain it and clean it?
My concern with draining it is that here in Florida the water table is pretty high and I am worried that I may float the pool.
I would appreciate your advice
Thanks

Is the pump hooked up and running? Do you have a vacuum?

The pump is hooked up and running with a cartridge filter, but no vacuum

Don't drain it.

Do get a leaf master type unit, like this one:
http://www.amazon.com/Poolmaster-28300-Sucker-Leaf-Vacuum/dp/B0007PZN9Qref=as_li_tf_tl?ie=UTF8&tag=poolbooks

Run your pump 24/7

Will the leaf master take care of the dirt also or just the leaves? If not, how do I get rid of the dirt that I cant see which keeps consuming my bleach/chlorine?
I have tried to keep the pump running 24/7 but after about an hour I must clean the filter as it gets clogged very fast.

It's probably not practical to remove the dirt -- they have a fine bag, but it may clog too quickly for you. As far as filtering . . . your type of situation is one of the best arguments for a sand filter, which is EASY to clean.

Anyhow, a possible clean up process for you is -- unfortunately -- long. If you could safely drain it . . . but you can't!

So:
1. Remove leaves.
2. Decide whether you want to remove the dirt with the filter (easier, with the leaves gone) or by buying / setting up a vacuum system, which could be a bypass to waste on your filter.
3a. Allow pool debris to settle and then vacuum to waste. THEN go to 3b.
3b. Chlorinate, filter, and clean filter till clear. (Start here, if you don't want to vacuum).

By the way, once you start chlorinating, too much chlorine is probably not enough! You do NOT want to add a little, wait, add a little more, let the sludge recover from the injury, and add more. With a concrete pool, you can go to Sams Club, buy 50# of dichlor, turn your pump on to circulate it . . . and dump 20# or more in. Then brush the pool throroughly. IF you have already removed leaves and some sludge, that may be enough.

But, if the pool does not look a LOT better in a day, you'll need to add more.

We'll need pool dimensions, to calculate volume and a starting dose (~100 ppm chlorine).