Quiet a job for another and now new job feel through because of error made on new job

I went on two job interviews for a TA position in an Elementary school. After second interview the Vice Principle called me on the phone and offered me the job. I accepted the job and was told Personnel would call me with further information. I told the Vice Principle I could not start for two weeks because I had to give my former job two weeks notice. He said he understood and that would not be a problem. I gave my notice and worked my last two weeks. I still did not hear from Personnel. I connected the Vice Principle and said he would look into this. It went on for about 5 days. Finally i get a call from Personnel and they in form me that I am not qualified for the job, because I do not have a college degree. After two interviews and I gave them a resume and filled out an application and never stated on this that I had a college degree. Nor was I asked at the time of interview. So know I have no job because I quit after the job was offered to me. Do I have any legal rights?