What recourse do I have regarding unemployment?

I left a part time position to accept a full time position with another employer. After less than a week, I was fired from the full time position. The employer said that it just wasn't working out. I filed for unemployment and was turned down because the latter employer lied on the questionnaire and said I was only hired part time. I have appealed this decision but it has already been two months and I'm getting desperate. When I was hired, I did not sign any paperwork; W-2's, acceptance letter, etc...There was never a discussion about policies and procedures or employer expectations. The only paperwork that I have is a copy of the personal check that she wrote me and check did not have taxes taken out and salary was less than what was verbally agreed upon.