This is a very difficult situation and I am truly sorry for what you're going through. The problem is that your employer did not violate any law by not renewing your contract. You would only have a legal claim if you could somehow prove that the reason you were not renewed was a legally protected trait (race, religion, gender, etc.) or retaliation for engaging in certain forms of legally protected conduct (filing a wage claim, taking FMLA leave, etc.). Otherwise, it doesn't matter whether the basis for termination is fair, reasonable or even true.
As for not getting responses to your job applications, that may or may not be because of what your old school is saying about you when new schools perform a reference check. You could find out exactly what is being said by having a friend pose as a school and request a reference, or hire a private detective to do the same. But the problem is that unless the school is making factually untrue statements about you, you do not have any recourse for a bad reference as there is no law that prohibits employers from making true statements of fact (even if unflattering) or ANY statement of opinion, no matter how negative. So, a former employer could literally say you are the worst employee they've ever had and you would not have any recourse under the law because that is a completely subjective statement of opinion and as such not actionable on a defamation theory or any other legal theory.
What you COULD do if you do find out they are saying bad things about you is retain a lawyer to send a cease and desist letter threatening a defamation suit. But for the reasons explained above, it would be essentially an empty threat unless they were making actual false statements about you.
I realize these options aren't great and that the news I am providing you is less than optimal, but I do trust that you will appreciate an honest and direct answer to your question here. I wish I could control the law, but I can explain explain how the law applies to your situation.
If I can clarify anything at all for you, please do not hesitate to ask. It is my pleasure to assist you further if necessary....