Your options regarding dealing with a contractor who won't fix your home can vary dramatically. The key is, do you have a contract with him, is that contract enforceable, and is his action in breach of that contract?
Exploring Your Options
If you had a contract with the contractor stating that he would do a set amount of work for a set amount of money and you've paid that money and he hasn't done the work, then he is in breach of the contract. In this case, you have several options:
If you have a contract and you have gone over budget, changed the terms of the contract or otherwise breached your agreement or altered it in any way, then you may need to pay the contractor more money or otherwise modify the deal that you had. If you're way over budget, for example, then the contractor may not be obligated to finish the work unless you pay for your cost overruns.
If you didn't have a contract, then things become a lot stickier. If you've already paid him some money and he hasn't do what he's promised for it, you may have a cause of action for unjust enrichment. This would mean that you paid him, thus enriching him, and he should not be able to keep that money without performing the work that you bargained for.
Getting Help
In reality, the three scenarios listed above are just a few and there could be many more that apply. The best option you have is to talk to a lawyer. Give your attorney the specifics of what has gone on, and allow him to evaluate your case and give you details about exactly what choices are available to you.