Legal Question in Landlord & Tenant Law in Illinois

If this is what the lease say, no. Under general Illinois lease law, rent is called an "independent covenant" which has many ramifications. Among them is that rent may not be tied to when possession is allowed. However, I would still make the argument that you can't charge rent if possession is not given, since that is fundamental to the concept of any tenancy and should trump the independent covenant concept. HOWEVER, starting out with the landlord on the wrong foot, meaning raising issues such as discrimination (I see no basis for this in your facts) will most likely just get the landlord "angry" and less disposed to working anything out, and a lawsuit would certainly not be helpful. My daughter attended UofI too and had a lease that was similar - occupancy for 9 months but rental payable for 12, which is about par for the course down there and the understanding was that rent was "diluted"; we never made a stink because that's the way most landlords who are willing to lease to students structure their leases. About the only thing I can suggest short of WWII is asking the landlord if some "additional" consideration for the 4 days would do the trick.