Well, hmm. Let's think about this. How would it really work out?

First, a few basics:
The Hunger Games are manipulated from behind the scenes. Who goes, as well as who "wins", are both heavily influenced by the people running the games, and their goal is to put on a good show. It's sadistic, deadly reality TV with unwilling participants.

People aren't chosen as tributes unless they make it to the age of eleven. It seems obvious, but it also means that if a person's disability prevents them from surviving to the age of eleven, they wouldn't be chosen as a tribute. You would have to choose a disability that would let that child survive, plausibly, in their home environment. If the child is visibly disabled and others can tell they will not be able to work, their parents (or other friends/family) need to be very much on their side, because this isn't a world that's kind to disabled District kids.

Each district has a different culture, and different things seem to be valued. District 3 may allow a physically disabled but intelligent child to survive because they are good with electronics; District 10 may be a luckier birthplace for a mentally disabled but physically healthy child who can care for livestock.

Some disabilities may be more likely to occur in some areas. People from Districts 9 and 11 may be exposed to pesticides; District 4, mercury from fish. Malnutrition in mothers and children can result in various nutritional deficiency diseases and congenital problems.

Wherever your character was born, you would have to make sure that they had a way to survive there, whether it was because they had family support, could hide their disability, or got lucky and were born somewhere where their skills could persuade overseers that they were useful despite it.

When it comes to actually becoming a tribute, you have to assume that the gamemakers have some level of control over who is chosen and who isn't. Would they deliberately exclude a disabled child--or perhaps deliberately choose them? If this is a disabled child who has survived because they are well-loved and their community has been fighting to keep them safe, why did no one else volunteer?

Then it comes to how this child is presented to the world. With the Capitol as it is, I would expect them to be presented much the way Rue was--as an innocent for the audience to feel sympathy for. Depending on the child's temperament, this could be something that the reader could see as an obvious front, simply because this is a child who is already a survivor who has had to be creative to make a place for themselves. They could even try to evade being put into the Hunger Games somehow--perhaps by escaping when people assumed they couldn't move far enough on their own, or thinking up tricks that others thought they were too stupid to figure out.

This person might have an interesting perspective on the world--might know better than most tributes that the Capitol is the real enemy. Or they might be bitter and see everyone as an enemy, period. Or they might be good at making friends, and rely on social connections to survive. How they try to survive in the arena is going to be closely related to how they survived in their district.

Would the gamemakers accommodate physical and sensory disabilities? Possibly. But they don't miss a chance to be sadistic and to manipulate their tributes. A child who used a wheelchair might be given one to use--but it might be completely inappropriate for the terrain, or it might be rigged to fall apart after a short while. Manipulating the child by tempting them with decent transportation would be easy, and the spectacle of that child trying to jump through those hoops would make for good viewing. For a physically disabled child who can team up with others for protection and transportation, it's highly likely that the gamemakers will manufacture a situation where the child's allies have to decide whether to leave them behind. Maybe they do and the child survives anyway. Maybe they don't. Maybe it leads to drama in the group. It all makes for a good show.

Would a child with a disability be "allowed" to win? No. Almost certainly not. The reasoning is simple: The Capital wants to prove their dominance to the districts, and if a child with a disability wins, it means that someone who seems "weak" (even though they may not actually be) can beat the Capital at their own game. That's not a message they want getting out.

If such a child managed to "win", or escape the arena, the Capital would have a lot of mud on its face. It would actually be a rather similar situation to what happened when Katniss and Peeta broke the one-winner-only rule, with the exception that the surviving child would be the only survivor. For that child there would be even less to celebrate than Katniss had, since unlike Katniss they would not have been able to save anyone else.

I've only read the book like five times, but I can't believe I forgot about that.

http://www.quora.com/Why-did-they-change-the-ending-in-regard-to-Peetas-leg-in-The-Hunger-Games-movie

You might want to read the answer by Cristina Hartmann, who makes some very good points about disability as a theme in the books versus the movie.

First of all: Movie adaptations are problematic. Movie producers don't really think about the prevalence of disability in real life, nor do they hire enough disabled actors, even in crowd scenes. The fact that the people in the movies are practically all non-disabled is an artifact of Hollywood.

There are, however, disabled people in the books. Katniss's mother is the most notable one I can think of, with her severe depression. Using that as an example, I conclude that in the poorer districts, disabled people are cared for and supported by family--and, if they don't have family, become homeless and quickly die because they cannot work.

Another thing you guys might be forgetting: The Reaping is often rigged. Would they choose a disabled child, or would they fudge it? That depends on which option made for good drama.

I'm a Master of Chemistry, but didn't have to defend my final project.

... is what I was about to say. Then I remembered that actually, there was a presentation in there somewhere. But it either wasn't a big deal, or I'm forgetting it in self-defence. So okay, it was there... apparently 'yes necessarily'.

(I had seriously forgotten that presentation until right then. I'm still not entirely sure it was in my final year at all, though... maybe I'm misremembering)

hS waffles