laylab, welcome to FT!

If you do not get on a flight, as others have already said, all subsequent flights will be canceled. Airline computers are very good at doing this, you will not sneak through.

Buy a separate ticket from Fort Lauderdale to New Orleans or, if there are three or four of you, rent a car at Fort Lauderdale and drive to New Orleans (if you have a day to spare). If you return the car in Orlando, it will probably minimize drop charges.

Unfortunately, you bought a non-refundable, non-changeable ticket and you will have to live with the consequences.