Can you get unemployment if your employer (untruly) states you were PRN an unavailable to work?

Hi..I have been working at my job for the last two years. Recently I applied for school and was accepted to attend full time. I advised my job that I would start school full time in January and asked to go PRN. My job stated that would be fine. I put in my two weeks notice and adviced I would remain full time to December 16th. We'll they mailed me out a separation notice that states I was employed from 1-17-13 - 12-16-14. The reason for separation states PRN status- unavailable to work. This reason is not true because I never stated that I was unavailable to work. I advised them that I would have three days off from school during the week and I would be able to pick up hours then. I would like to know if it would be possible for me to draw unemployment...seeming that I never quit my job. Thanks