I was refused unemployment after being let go for unproffesionalism(complaints of a coworker)

I was called to HR and told I was on investigative leave. The next day they called and let me go. 8 weeks later the unemployment office said that the company said I was fired for unproffesional behavior for multiple incidents and had complaints by a coworker about a conversation about a TV show and a statement about a vjj. What the company did not ask was that that employee asked me about the vjj initiating the conversation. This dept. often participated in such loose conversations & statements. It seems to me that I was picked out by a co worker that just didn't like me as much as she like the others in the dept. I really did not get the chance to defend myself or correct an offense that I was not aware happened. I now just want to reiceve unemployment while I seach for a new job.
I worked for Charter Communications in a call center. I had been there almost 2 years in several dept. and was a good worker w/a successful stats and no such problems in the other depts. How can I win a fight w the unemployment office?