Illinois does not have any state laws on rent withholding or repair and deduct remedies that apply across-the-board to tenants. Some remedies are available in utility termination situations only.
For an overview of Illinois landlord-tenant law, including your rights to habitability, see: http://www.law.siu.edu/selfhelp/info/property/Landlord-Tenant%20Rights%20in%20IL.pdf and http://illinoisattorneygeneral.gov/consumers/landlordtenantrights0404.pdf.
Also, check your local housing ordinances for any city or county rules that cover tenant rights when it comes to repairs. Contact your local building or housing authority. To find yours, call your mayor or city manager’s office or check your city or county website.