Yes, it sounds like you should be paid for that first hour in the morning as well as your overtime. Sit down with an experienced employment attorney to learn more about your rights and remember, the consultation for this kind of work should be free and the attorney should charge you no more than 33% of what he or she is able to obtain for you.
This answer does not constitute legal advice and you should contact an attorney to confirm or research further any statements made in this answer. Any statements of fact or law I have made in this answer pertain solely to New York State and should not be relied upon in any way in any other jurisdiction. Additionally, we also encourage you to reach out to us via Twitter (https://twitter.com/#!/WhiteRoseMarks) or Facebook (http://www.facebook.com/WhiteRoseMarks) if you have follow up questions as we do not monitor questions after providing an initial answer.
This is known as "off the clock" time and is frequently abused. You are entitled to overtime pay after 40 hours per week, from the time you are required to show up, even if you do not start work until later.
Your employer is violating the Federal law known as the Fair Labor Standards Act (aka "FLSA"). You could bring an action for all prior back pay and overtime as well as attorney fees and punitive damages as well. I recommend you seek out an employment lawyer and consider your options.
My answer is not intended to be giving legal advice and this topic can be a complex area where the advice of a licensed attorney in your State should be obtained. Please click "helpful" or "best answer" if my answer added any value or add a "comment" if you have more info for me to help you get a better answer.