One of the requirement to be eligible for unemployment benefits is to be "able and available" for employment. As long as you are currently able and available for work you still should be eligible for benefits. However, once you have committed to starting a business and are no longer available for work you may become ineligible.
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The Board of Review makes its decision based upon the record of your case which includes any documentation provided by the employer, the summary of the adjudicator (the first person you spoke to from unemployment) and the transcript of the telephone hearing. You will receive notice that an appeal is pending. Request a copy of the transcript and submit a written argument in response to the employer's appeal. The time frames are short so don't wait once you receive notice.
If the agency has 5 employees or more you can file a complaint with the Illinois Department of Labor. You can go to the website and there are fillable PDF forms that must be mailed to the IDOL. The agency is violating the Wage Payment and Collection Act.
In a word, no there is nothing that can be done short of getting your old job back. From what you have stated in your question it does not appear that the school district acted in bad faith when it offered you the position. The type of position that you applied for is dependent upon the number of students who need the services. Keep trying to contact your former employer.
Your question is difficult to answer without more information. FMLA can be taken on an intermittent basis. Also, an employer can designate leave time as FMLA leave. Are you on leave now? If so, for how long?