I don't think you have to buy the car new for Texas lemon laws to apply. According to the statute,

(2) "Owner" means a person who:
(A) purchased a motor vehicle at retail from a license holder and is entitled to enforce a manufacturer's warranty with respect to the vehicle;

If you bought it from a dealer and it still has the new car warranty, then you should qualify. However, the time limit for the car being out of operation doesn't count if you have a loaner car. So until they have attempted to fix it four times, you probably don't have a lemon law case.
http://www.dot.state.tx.us/mvd/lemon/statute.htm