svHyLyte and DavidM are right on. Sounds like you have a combination of things working against you, all caused by moisture.
When trees grow they absorb water-soluable minerals which are then deposited in the wood. Being water soluable they dissolve again when the wood gets wet and they migrate to the surface where they are deposited as the moisture evaporates. This makes dark brownish stains. Second, moist wood is a playground for mildew (there are over 1,000 forms of the stuff) and when it grows it makes the area look black or dark gray. I think you have a combination of these two.
First you must get the wood DRY .... REALLY dry. All of the finish must be removed to accomplish this so the moisture can evaporate. If you can get the wood out into the open where sunlight can get to it and air can circulate all around it it will dry much quicker. If you leave it in place at least run a fan at low speed over it. In place the drying could take several days.
Once dry, one of the two step teak conditioning kits would work - one step to remove the stains, the second to kill the mildew spores and bleach the wood back toward its original color. Use step two sparingly so as to avoid over-lightening the wood.
Once the stains have been removed you must first make certain that the source of the original water is stopped, and ideally the BACKS of the boards should be treated with a water-repelling oil
treatment. then, and only then, should you refinish the tops of the boards using a good polyurethane
finish. You'll probably never get the whole floor to march completely, but this should at least make if look good again.