If you buy a new TV it would not need a convertor box. The over the air antenna has not changed...only how the TV processes the signal. If you plugged a brand new 24" LCD TV where the 15" was and plug the antenna in...you would get digital signals.
PLEASE do not send questions via Private Message, my inbox fills up too quickly. Post questions in the forum as a new thread so that other users can benefit from the answers. Use Private Messages for sensitive information only (VIN, Contact info or things you do not want the public to see).