Fired for asking for back wages

1) You are certainly entitled to back wages: when you worked, you must be paid. You can think of it this way: when you did the work, you did so under an agreement (even if it was only an oral, or unwritten one) according to which you would be paid a certain amount for each hour of work. There was effectively a contract (again, even if only an oral one) between you and the employer. If you did your part (you did the work), then they are contractually obligated to do their part and pay you. They are also not allowed to be "unjustly enriched" by knowingly getting or accepting the benefit of your work, which was done in expectation of being paid, for free. Therefore, in addition to your rights under the labor laws, you have at least two other legal bases to insist on payment.
2) Contacting the department of labor is the right thing to try: the department could help you get paid as long as you were an actual employee, not an independent contractor. If they don't, however, you could also sue your employer for the money they owe (based on "breach of contract" and "unjust enrichment"), such as in small claims court.
3) As a general matter, if you don't have a written employment contract, you are an "employee at will" and may be terminated at any time, for any reason. That said, you have some protection from being terminated for trying to enforce your legal rights, such as to be paid for work you did. You should add to your claim with the labor department, or your law suit, if you end up suing personally, a claim for additional compensation for "wrongful termination"--for being fired for trying to vindicate your legal rights.