For unemployment in NM, what must I prove if I claim I was wrongfully fired?

I worked for a friend and I believe I was wrongfully fired. As the store manager and lead sales-rep, I had an optional extra work day and decided to take it off. After the fact, I was told I was fired for no-show. In my claim of wrongful firing I could bring up the fact that I was not paid on-time more then a handful of times. My schedual was constantly edited without my knowledge, and I wasn't being paid what I was supposed to be at one point. The owner would fail to even keep the electricity and water on. Does any of that matter when filing for unemployment?