I had a similar problem and posted this exact same question back on the GardenWeb boards. The general consensus was that it was a rot. Most that commented said that basil is a very difficult herb to get to survive an extended period of time indoors. The plant I had lasted months outdoors in a pot just like that. Within a month or so of coming indoors to winter my leaved browned and the plant began to die.

awww :( Well, its the first time I tried growing in doors :D I have 4 more pots that just germinated, see how will they do :D

I germinated mine as well. As I said before everything seem to start off good it was towards the end once they came inside when everything went downhill. I scoured my computer to try to find some photos that I had put up on the gardenweb so that you could compare your plans with mine. However I can't seem to find those photos but if I do remember it looked quite similar.

I cant grow them outside, I live in Scotland :D Maybe in the summer, in the greenhouse... But not outside :) Last time I gave it a chance it just slowly shrank and died :))))

Mohort - even down here I grow my basil in the greenhouse all summer. It just doesn't get enough heat outside to thrive. I don't even attempt it in the winter. Just makes Basil season all the more enjoyable.