Employment Law Questions? Ask an Employment Lawyer.
Unfortunately, you are in a bad state for this to happen in. Most states have a "wage claim" process through their department of labor that is free. The DOL handles the investigation and enforcement. They do that intentionally, understanding that the cost of going to court makes it impractical when you are talking about a smaller amount of money.
Your state though doesn't do that and they leave it to you to handle on your own.
So, you have to file a suit against the employer. You need to give them a written demand first, stating that they must pay you. You need that written demand because the court counts the days that the employer hasn't paid from the date of the demand. I think it is reasonable for you to use the date that you signed their form though, asking for pay. You could allude to that date (or approximate date) in another letter demanding the pay.
Under LA Revised Statute 23:631, the employer can be fined by the court up to one full day of pay for each day they don't pay you what you are owed (up to 90 days of fines). This fine is supposed to make up for your having to sue. You could file in small claims court to make it cost effective and fast.