Quoting Damon Salvatore:" I got a great job offer with another company, so I quit my current job (well I gave 2.5 weeks notice) ... [snip!] ... if I can prove that I wasn't a no call no show that I can have the job, but I have no idea how to do that. Can anyone help?"
I would personally have someone you have worked with in the past tell them how reliable you are and that they have known you for x-amount to time and that you have always been responsible, reliable, and hard working and that that person you worked for was a hateful person or something like that.