How brown is brown? Is the main stalk shriveled and dry? Are the leaves crackling and turn to dust? Or is there still some life in the plant, somewhere, somehow?
I found a rare Valencia Heirloom plant recently at my big box grocery store and it was pretty far gone -- but it's a whole lot better now, 1.5 weeks or so after I bought it. I'll tell you what I did (and if you want to read my thread, I got some *very* helpful advice, which I'm sure will apply to you too), and hopefully what I did will help.
If you want to try to save it, the first thing is to get rid of the tomato, as hard as that will be to do. My Valencia had flowers on it, and I *hated* to get rid of them, but I had to. Right now you want your tomato to focus on staying alive, and then to produce healthy foliage and stalks. Fruit can come later, once you've nursed the plant back to health!
Secondly, you want to get it into a healthy environment as soon as possible. That means, LOTS of water, good soil with lots of nutrients, and plenty of warm sunshine. Because I was getting married the next day after I bought the Valencia, I set it out in the sunshine (the store had it under a patio covering -- it *never* got sun), in a BIG serving platter filled with about 2-3" of water. I set the tomato, in its pot, in the water, and just let it soak up the water from the bottom up, hoping that that would suffice until I could really get to it. The soil in the pot was worse than bone dry, so the plant was starving in addition to being deprived of sun. Sun and water alone made my plant perk up a little.
The day after I got married, I transplanted the Valencia into my garden. I got some bone meal as recommended to me, tossed some of it around and in the bottom of the hole, carefully crumbled the 'soil' apart so that I could free the roots (by then, the entire soil in the one gallon pot had become one giant root ball), and planted the Valencia in the hole pretty deeply, and more deeply than it was originally in the pot, by quite a few inches. I then used compost and a (very) wee bit of balanced 10-10-10 fertilizer around the plant when I filled the hole back in. I didn't want to burn it, but I knew it needed nutrients. Then I watered the HECK out of it!!! I continued to water the heck out of the Valencia for the next few days, because no matter how much I watered it, that poor starving plant took all I could give it. My educated guess is that it sucked up a good 6" of water in 3 days. I know that sounds like overwatering, but it wasn't -- my Valencia was just that badly off. I also bought a 36" stake and a 24" stake and staked it upright, hoping that the uprightness would help the plant recover. It seemed logical to me!
Now, a week and a half after I transplanted and about 2 weeks after I bought it, I know my Valencia is happy. It's producing new leaves at a great rate and even a few new baby stems here and there. I had to finally pinch off some of the original foliage that was really dead and not coming back, but those so far have been rare. The original stalk is becoming a healthy green and the offshoot stalks are not drooping any more. Most of the original leaves have uncurled or are in the process of uncurling, and the new foliage is just growing by leaps and bounds. As a matter of fact, I've had to pinch off two new sets of blossoms! My Valencia obviously wants to make tomatoes, but I want it to focus on getting really healthy and growing some first. Right now it's just barely able to support any tomatoes, so it needs to really get a bit more sturdy. And it's stunted too -- I don't know how much taller or whatever it will grow, seems silly, but here in 4a there's not that much time left until first frost, relatively speaking. Based on how long it's taken my other tomatoes, I may only get a few from the Valencia, if I get any at all, we'll see.
Anyhow, that's what I did and my plant is recovering nicely from it's grocery-store nightmare. Hope my story helps you!