Unfortunately Illinois is about the most impossible state in the union for obtaining a title. The Sec of States view is if you don't have a title you shouldn't have the vehicle.....it is against the law here to buy without title

You have to fill out crap paperwork, pay mucho fees and find an insurance carrier to buy a title bond policy for the full value of the vehicle.....they will check for the highest book possible. Or, you can put up a cash bond I believe. It will be at least three years minimum before you can expect the title...if they give you one. They will contact the last registered owner if possible and guess what....if that person says they still have ownership you can expect them to come pick up the vehicle from you.....you are out your fees, any money you put in the vehicle, your cash bond or title policy premiums etc. This happens more and more as certain vehicle become valuable. Vehicles do drop off the Illinois system around fifteen years after it was last registered/had tags purchased, but, you can't guarantee it.
I would start by running an NICB vin check to see if shows as stolen....or if you know anyone in law enforcement have them do it for you. Then, have someone you know in a title friendly state register it and then "sell" it to you or go with one of the scenarios like Vermont. About the only way to do it in Illinois in a reasonable way is if someone you know owns a licensed tow truck and/or scrapyard/service garage. They are allowed to file for a mechanics lien or abandoned vehicle lien (now with an abandoned vehicle the tow operator has to get a cop involved but all tow drivers are friends with cops).....they can have a title in a few weeks but you still pay for their time/fees and still have to pay your own inflated registration. Sorry to be so long but if you don't know someone in the biz go out of state.