I should add that if I add water, it seems that most of the water runs right through the pot and is not absorbed by either the soil or the plant (the soil remains moist, however, so it just might be at carrying capacity while the plant is not absorbing any water).

In addition, I have yellow stains on the floor where the water came out of the pot which appear to be a non-water soluble salt.

I don't know if any of this helps but I figured I should give anyone reading this post as much information as possible.

Well to begin with Bananas need sun and lots of it. If you can't provide sun for it in your current location then you are simply wasting your time in trying to save it. Can you locate it somewhere for more light?

1) You need sun,
2) you have over watered or underwatered, or
3) there is more to the story.

well, I wish I could provide more sun to my plant but, unfortunately, that is impossible at the apartment I'm living at currently. The aparment isn't mine, I don't have a yard, and it's surrounded by buildings and vegetation so it has shade most of the day =(

Stop watering for a week.See if you can find a grow lamp and give it about 4-6 hrs of light and place it where it gets air circulation.That is all you can do.If nothing happens in a month, I would throw it away or give it to some one who can give it 4 hrs of sun light.
michelle

I think that your plant is so used to the Florida sun and now that it's not in the sun as much coupled with the fact you're still watering as if it were is leading to root rotting. Cut back on the water about 50-60 percent and see what happens.

Well, I haven't watered the plant in a week now and it's getting a new leaf!! Yay! Should I cut it back though? (Because of the ceiling) and how much water should I ideally be giving to the plant?

Thanks for all the help!

Banana's like sun. More the better. If you can find a patio to put it on - either there or at a friend's/family's flat, that would do the trick. I would let it go to only slightly moist - lack of sun and excess moisture will produce rot. Trying to use plantlights for a nanner can work - but only as a temporary solution - nothing beats the intensity of sunlight...