I attended a doctoral program and was completing it in 3 to 4 years. I got a life-threatening sickness that set me back several years. When nearing my dissertation I was dismissed. I was told that I was let go because I had cancer. I never wanted to return to that school again, but not having completed my work has caused me great heartache and I am not able to pursue the career I desired. Is it at all possible to complete the degree elsewhere?
In general, I think graduate schools want students to pursue their entire PhD candidacy at a given institution. Moreover, schools may be reluctant to count work done a long time ago as part of the requirements for obtaining a degree, as it likely sets a bad precedent.
Moreover, there's the question of financing. If you're in a program where students are financed through TA's, it's a lot easier to convince a school to take a chance, rather than in the sciences. The reason for this is that funding in the sciences is often tied to specific projects—which means that you will most likely need to change topics if you pursue a PhD in such a department. This would of course set your time to degree back considerably.
That said, you may find a sympathetic department that's willing to take a chance. My best advice is try to talk to the graduate admissions officers of some of the departments you're thinking of applying to. They'll help you to figure out what are the requirements and possibilities.
This situation surprises me: in the U.S., one could likely file (and win) a lawsuit alleging discrimination, in such a situation.
Dismissal from a college or university on grounds that one is ill is not legal, I think. Accommodation must be made, so that perhaps things are delayed, but not simply cancelled.
Outright dismissal from a job (such as research assistant or teaching assistant) on medical grounds I think is not allowed, either. One may be required to take a leave of absence if one absolutely cannot do one's job even with accommodation, but there is substantial legal (and moral) push to accommodate and reach a compromise.
I think discrimination on admissions, on medical grounds, would also be essentially illegal.
Edit: you should talk to a laywer conversant with such things, who might be willing to talk to you without a huge fee if you describe your situation to their screening personnel. The situation is rife with lawyerism, indeed. Be careful.
I think you should try to fight it diplomatically but legally with the school. It doesn't seem fair or legal. It would be nearly impossible to continue in another institution unless you have relationships and also the reputation of the former school is considerably higher, which you wouldn't want to do anyway.
Depends if really the time you were away was strictly due to sickness. If you took several years more afterwards it is unlikely for you to win. Doctoral programs routinely turn away people who started, left, went to the real world, didn't like it, and want to return. They believe that somewhat freshness of knowledge and being current in the topics is important. Also they have some strange ideas about academic virginity that you want to take into account.