The short answer is "According to the contract".
Generally it is understood that deposits cannot be used for other projects, but this is typically hard to prove in a court. If the contractor uses a general fund, unless that fund can be shown to be less than your deposit, with absolutely no work done on your project, only then can you argue that he used your funds for another project. Getting this information requires legal help.
But there are several variables. You notified him that he breached; did you do it as the contract required (in writing, to a specific address, proof of reciept, etc)? What was the breach? When he did not show up; did he call or contact you? Does your contract stipulate when the work must start by? If the contractor was a week late, but called you to say he'd be around in a few weeks you will have a hard time claiming breach unless your contract had a hard date agreed by both parties.
Looking at a worse case situation where the contractor no longer wants to work with you and is prepared to fight:
Hiring a lawyer will mean you will pay almost all the money the contractor took as a deposit for legal fees, win or lose. So by going to court, with legal counsel, you stand to lose over $6,000 all told.
What will probably happen at district court is you will go into the courtroom and the contractor will have a lawyer (probably provided by his insurance company; IE very experienced in this type of case). Even if he does not have a lawyer, he probably has been through the courts before and will be pretty well versed on how to handle it. If you do not have a lawyer, consider getting one so you are not ambushed.
During the presentation of facts, the contractor will most likely produce the contract (and point out if a hard start date was set or if there were exemptions, etc) and a list of materials ordered and copies of permit applications and permit fees paid. If the contract stipulates it, he may also have his hours spent on court preparation and legal fees included. If the contractor provided the contract for you to sign (without a third party) odds are good the contract is heavily in his favor. The only real costs you can argue are those that were incurred after your correct notice of breach (except court costs).
So in the end, the contractor will probably be able to easily show at least $3,500 in pre-work. Even if the judge rules in your favor, he/she will award you nothing but any raw materials (or their value if they can be returned) the contractor claimed are for your project. Unless the contractor counter-sues, you typically do not get charged additional costs (with court costs being the exception).
As you can see a well-written contract is your best defense. Using a third party project manager is also a way to protect yourself in the future. Usually a licensed architect can provide construction management; they will oversee the project, provide a proven (AIA) contract and can ensure that if the contractor is in breach it is handled correctly, and a replacement contractor is located to keep your project moving forward.
Even though you are going through a general district court I recommend you do not enter the courtroom alone; hire a lawyer. Be prepared for the contractor to argue the money is gone because of your project, to push the court date back or for the contractor to not show at all. (This doesn't mean you win, it means a notice will be sent via Sheriff / police requiring the contractor to show up again at the next set court date. If they miss the second call, they face other fines / charges, but in reality there is little punishment and it buys them 30+ days longer with your money. Plus the notice must be received; so if the contractor can avoid the police notice, he draws the court date out indefinetely.)
In the end, even if you win, all you have is a court order that says the contractor owes you money. Getting the money is another long battle, that requires you to do all the work and take each required step before the court (via the police) will go after the contractor on your behalf. So as you can see, even if you win, don't plan on a check being written at the courthouse.
If there is anyway to resolve the breach and get the contractor to agree to return to the project, consider it. If you trusted the contractor before and his work has been good; he may be bad at time management but good at his work. If you have a professional 3rd party project manager to run the project, this will give both you and the contractor protection for the duration of the project, and the cost is minimal compared to the peace-of-mind and quality assurances you will receive. Make the offer to the contractor to use a 3rd Party project manager, get a hard start date, and work with him to prepare a new contract or amended contract that both of you can live with. Neither of you want to go to court, and it is in your interest not to go to court.