Marilyn,
Hello! Never fear! There is hope for your plant! It most likely looks "lifeless", in your words, due to the fact that it would much rather be outside. Bananas are meant to be outdoors. You can certainly do this with a few precautions.
First, I'd repot it in something a little less free-draining. You don't want a soggy soil mix, but bananas enjoy moisture, so I don't feel that the gravel and charcoal are necessary; at least not in large amounts.
Secondly, try to put it outside somewhere where it doesn't even really get any direct sunlight at first. A covered patio, in the shade of a large tree, or the north side of your house would be a good place to start. The reason for this is that even in these areas, the light is brighter than it is indoors. Leave it in this location for about a week.
Third, slowly move it to where it will get a little direct light. By a little I mean maybe 1/2 an hour at first. Do this for several days. If you can gradually expose it to more and more light it should be OK with 6-8 hours or more a day within a month.
The reason you have to do this is that the leaves that emerged indoors will not be able to withstand the sun and will burn severely. Leaves that emerge outdoors will be accustomed to the sun with no problem. Also, be aware that if you have much wind that the indoor leaves will probably not survive the wind, but all new leaves will be much stronger.
As for the leaves turning brown, I wouldn't worry too much as it sounds like the natural process bananas go through to me. Let the remaining leaf sheath turn brown then pull down and either cut it off near the base or tear it diagonally and it should pull right off. You can do this for all the old leaf sheaths if you'd like and it will eventually expose the fresh green pseudostem. You do have to be careful not to remove too much if the pseudostem is very skinny as that can cause it to snap in the wind too. You have to find a happy medium. However, if you have a dwarf variety (like Cavendish, Orinoco, or Brazilian) they have fairly stout trunks and you shouldn't have this problem. Good luck!
