Dug up a basil plant, potted it, and brought it in for winter -- now it's dying? Help!

Pretty much what the title said. I dug it up from the garden after a nice productive summer (it was the biggest of its siblings), potted it carefully, and left it in the shade. Then that evening as it was becoming dark and cold I brought it into the sunroom of my house, gave it a nice central position in front of a south-facing window next to some cactuses and aloe, on a shelf right above the radiant space heater, and watered it once since then. That was less than a week ago.

Now some of the lower leaves have turned yellow and started falling off, some of the others have brown spots, and in general it's looking a bit shriveled.

What should I do? Anything I can do? I want to have fresh basil all winter long!

It could be that the change in environment was too much. It's also possible that the plant had done its dash...I find basil is often a pretty short-lived herb. You can probably sow some seeds indoors and keep a few going that way.