I've just purchased a house with a 40x20 pool with spa.
Here is what I know:
The pool is about 8' at the deep end and about 4-5' a the shallow. No clue how many gallons that is.
It has two skimmers, a DE filter, a Lars heater, two Hayward pumps (one main and one booster), a chlorinator, which is connected by flexible plastic pipes and what appears to be a rain sensor?

Now, I don't know how long the pool has seat unused - Maybe for 2 seasons, but it does look like it needs lots of TLC.

I called the pool people and they came in, opened the pool, got everything going, shocked it and added algaeside.
They filled the filter with DE, took water sample (no results yet) and told me to keep it running for a few days, after which the filter must be backwashed and more DE added.

A couple of hours after they had left, while I was cleaning the bottom from large debris, the filter got clogged because the muck came up from the bottom. By the way, the bottom was totally black, but the water was very clear.
SO, I backwashed and decided not to add DE for now, until I was done stirring the bottom.
It ran w/o DE for a day, b/c I figured to let the filter catch all the larger stuff and add DE later to catch the rest.

After another day, I saw no results what so ever and desided, in my infinite wisdom, to open up the filter and see what's doing.

It was a horror show in there. The grids were completely overgrown with algae, so I took them out and hosed off the algae and the dirt.
Put the grids back, closed the filter, opened the pump to suck on the strainer and added DE.

Pooffff... DE comes shooting out of the jets...

At this point, I am hoping that I can still salvage the grids, 'coz they're pricey.

Also, looking at the walls and the bottom, I don't know if that kind of dirt/algae would ever clear up on its own.
I am seriously contemplating draining the pool, hitting it with a power washer and maybe even a little acid in some particularly nasty spots.

One other reason why I am thinking of doing this is the fact that lots of tiles have fallen off at the water line. This will give me a chance to fix them.

Any way, long first post, but you can probably tell that I am overwhelmed with the task at hand

Where should I begin?
Thanks in advance for the help!