Can I get my job back?

I was terminated from an employer due to a recommendation from an EAP counselor, saying I was "non-compliant" with they had set up for me at my employer's request. What made me " non-compliant" to this program was calling to check in with this counselor on a Sunday. Sunday's were considered the previous week, which had never been made clear to me previously. I had been following the program laid out for me to a tee for about 7 months. When this happened, the counselor waited to let me know I didn't check in correctly until the following week, meaning that I hadn't made my weekly check in and so she reported me and I was terminated the following week. I filed for unemployment, which was rejected by my previous employer. I had a phone hearing with a judge and 2 representatives from the company, and the unemployment agency ruled in my favour. A year later, I applied to the company again and was offered an interview that was cancelled shortly after, and when I talked to an HR representative, I was told I would have to wait 36 months before I could apply again. It is now just a month shy of 4 years after my termination date, I applied and was given an opportunity to interview again. I recieved a phone call from the company letting me know that they were planning to send me an offer at my previous rate of pay. They called back shortly after to let me know that I was ineligible for rehire. When I asked what the reason for that was, they said there was nothing in my profile to let them know the reason OR to even let them know why I was terminated in the first place. I just want my job back. Other than this incident, this is a great company to work for. I enjoy the work and the benefits cannot be beat in the industry.
On a side note, I have worked with people at this company that have had incidents similar to mine, attendance issues, been terminated for sexual harassment, etc. And they were eligible to get their job back. I have never had an incident prior to this and I haven't had any incidents at any of my employer's since. Is there anything I can do to get this resolved in my favour?