Wrongful termination?

I had been hired through a temp agency to work at a factory. To do so i had to pass a drug screen and background check and i passed. Usually after 90 days with the temp agency the company will decide to hire you or let you go. Halfway through they decided to hire me early due to good work with another person. Again i had to do a drug screen and background check. A week later i went in and got sent home with a letter saying they were contemplating making a decision adverse to my employment interests. Basically saying i had been fired because i had 1 misdemeanor on my record. How can i pass the backgorund with the temp agency to get in, then the company fires me for the same reason. I know for unemployment you need to work 16 weeks. I had only been there for about 6 weeks. Is there anything i can do? wrongful termination possibly?