I was granted unemployment compensation and now my former employer is contesting that decision.

I was terminated from my position as a social worker in a local facility. There had been occasions when my employer wanted me to sign for payment for services that I did not provide. I am licensed, and felt that my license may have been compromised by signing such documents. As time went along my employer read some emails of mine to another co-worker where we discussed meeting to look for another employment opportunity. The meeting never took place, but my employer took my computer & terminated my employment stating that I was being terminated for looking for employment on company time. There were others at the time who were also terminated for this reason.
I was granted unemployment, then my former employer contested it. The unemployment bureau determined that I was not at fault & continued to compensate me. Now my employer wants to take me to court. They had 30 days to file an appeal, and did so after 29 days. What should my next step be? Thank yuo for any help you can give!
Becky