I'm asking for my job back after giving verbal notice (transit, company)

[cobarry]

This is my first time on here.
two years ago I was diagnosed with diabetes. I had called out sick just before I was diagnosed and was on the way to giving my two weeks notice. The HR rep. called and asked if I was going to give notice and I said yes, and he asked if I would like to give a verbal notice...well, idiot me said yes. I didn't think or understand I perhaps still had to give a written notice.
Well, after I had relocated to another state and got my diabetes under control, the company I went to work for, turned out to be not so good after about three months and I quit.
I called the HR in my previous state, and come to find out the old HR is no longer with the company. I stated that I would like to be considered for rehire, and was told they will not be hiring until next contract (I'm a transit worker). I told the new HR what had happened and was told "we'll talk about that when the time comes". I was also told to put my application in when they post for positions on the website. Is there a window possibly available for rehire? If so, what should I say or do to communicate of a miscommunication on the previous HR? Thanks

[observer53]

I'm a little confused. It was two years ago when you gave this verbal notice, you moved to another state, got the diabetes under control, had worked for another company about three months and quit, and then inquired of the company you left two years ago about rehire. Do I have it right so far?

Now, they don't have openings right now, but will be hiring when the next contract comes up, and they told you to put in an application.

You asked about a "window" for rehire.

Whether there is some sort of rehiriing "preference" for former employees, and the duration of that, varies from employer to employer. (I work for the state, and there is something like that under our personnel rules) Are you thinking that the preference for rehire with this employer (if there is one) may depend on whether you gave proper notice in the first place? Is that what the "miscommunication" is about?