Contract damages are those to put you in the position would have been if the contract would not have been breached. These are called compensatory damages. Purely contract claims do not generally qualify for punitive damages. I don't know what you mean by the "fee already' paid.
Most attorneys do not take contract matters on contingency unless the debt is secured and it is otherwise absolutely clear they can both win the case and then collect. Contingency is not common because the value of the damages may be low and even if you do win you still have to collect. The judgment debtor can file bankruptcy or just otherwise avoid paying. A contract claim is radically different than say, for example, auto accident litigation. In auto litigation the at-fault driver is usually rather clear and, because of insurance, it all but certain the attorney will get paid. This is not remotely similar to a contract claim.
Speak with a local litigation attorney and they can give you an idea if this case makes any sense and for an idea of the cost.
This answer is for informational purposes only and is not legal advice regarding your question and does not establish an attorney-client relationship.
In Texas, a breach of contract permits the non-breaching party to recover actual damages (such as the money paid), consequential and incidental damages (damages that are a foreseeable consequence of the breach), and reasonable and necessary attorney's fees. Depending on the facts, you may also be able to make a claim under the Texas Deceptive Trade Practices Act which permits recovery of treble damages in certain circumstances.
Depending on how much money is at issue, attorneys may be willing to accept a breach of contract case on a contingency basis, but there are other options as well (such as a contingent hybrid agreement). I have put a few links below that may help explain this a bit more.
I encourage you to reach out an attorney about your case.
In general, breach of contract entitles you to any damages you suffered as a result of the breach. In some cases, you can also get "specific performance", meaning compelling the other party to perform their side of the contract. Other remedies may be appropriate depending on the facts of the case and the nature of the contract.
Texas law allows parties to recover attorneys fees for breach of contract claims. Whether a particular attorney will choose to take the case on a contingency is very much going to depend on the case, the clients, the other party, and the attorney himself or herself. If I had to hazard a guess, I would say that most breach of contract cases involving commercial clients are not contingent. But, many cases involving individual consumers and small businesses are contingent because the client may not be able to afford the services otherwise.
In some cases, the attorney may agree to a reduced fee or a partial contingency fee.
The contingency would not typically be a straight percentage fee (like 40% of the damages), but would instead be hourly. Depending on the size of the damages at issue, sometimes the attorneys fees greatly exceed the amount in dispute between the parties.
You should take your particular situation to an attorney who practices in the legal area concerning your contract and get further information and get advice particular to your case and situation.
I am licensed only in Texas. Offering information of a general nature in response to a question is not intended to be legal advice in your state.
Whether or not an attorney would take a case on a contingency depends on the likelihood that you would prevail, the amount in controversy, and a number of other factors. Chasing the recovery of just your fee probably would not be enough to motivate an attorney to take the case. For example, if your fee was $10,000, and the new attorney had a 40% contingency, that would be only $4,000. Not a lot of litigation can occur for that amount of money. But you can negotiate the fee and the associated services. Perhaps you would agree to have a new attorney write a demand letter to see if the old attorney would refund the fee that you paid.
You may consider seeking help from the Dallas Bar Association fee dispute committee. You can review the web site at the following link:
Dallas Bar Association - Fee Disputes