How many hours a week are you going to be working for the school system? Regardless of when you are going to be paid? Also doesn't matter whether you are an hourly or a contractor. Amount earned weekly and availability is more the key. You should be fully eligible for unemployment until Jan 1,2010 when the job begins. They (NJ unemployment) should see it this way, because what they look at is wages earned and work done during each individual week you have filed for benefits.
This means even though you have the job to go to beginning in January, though you have already signed the contract, you should be able to draw unemployment insurance until the first week you actually work.
Then, you should figure up how many hours you will work, Sunday through Saturday, each week during your contract with the fitness program. If this is not full time, then you would still be eligible based on being able and available for full time work. Divide the total pay by the number of weeks in the contract. If the gross wage you make per week is less(by even one dollar) than your weekly unemployment payment, you should be able to continue filing each week, report this weekly wage and receive part of your unemployment benefit as well as your eventual pay for working here.
The money you do not receive from it (unemployment) each week because of your wages reported would be added on at the end of your claim, in other words, you do not lose this unemployment by working part time, you get to string it out over more weeks until the balance is paid.
But $480 a week is pretty significant. If it is more than your weekly unemployment amount, or if you honestly cannot say you would during this period be able and available for full time work in your field if it were offered to you, you will simply stop the claim for the amount of time that you are working for the school system (10 weeks). This is done by simply stopping the weekly certifications for benefits. You do not have to give formal notification you are stopping the claim. No certifications, no checks. Then when the job ends, you will contact the office and re-open your claim and pick up drawing benefits.
You have committed no fraud at this point. You did need to start this investigation by telling the NJ office about the circumstances of the contract which has not begun yet. Each week you are asked questions such as "Did you do any work for which you were paid or will be paid?" And then "Did you accept a job, quit a job, were you fired from a job...this week?" At some point when you did, you should have told them about accepting the job with the school system, but patti is right, this could have been a misunderstanding on your part, not an effort to mislead the unemployment system.
This is not the first time the New Jersey office people have experienced this or a similar situation. They will know you are not trying to break the bank or defraud them and should be very willing to explain things to you.
As I said, until you begin the job, you should be fully eligible for unemployment at this time, unless you were laid off from a school system in the first place. This opens another kettle of fish, known as "reasonable assurance" which is related only to school systems in some states. In any case, keep talking to the unemployment office, keep in mind that everything works by week, and it should be fairly easy to straighten out.