Congrats on your purchase! I ran into the same thing when I recently purchased my '67 Ambassador from a seller in Atlanta... the big service places and even the local A/S service center don't answer the phone and won't return your call. I was lucky to find a small service place the was willing to work with the seller on dropping off the trailer and checked the whole thing out to make it safe for the trip back to WI.
Best advice I can give you is to call every RV type service center you can get a number for... Ask a lot of questions about who might be able to do the work... it's very likely that there is someone in the Chicago area that will get your trailer checked out... the problem is finding this place.
Good luck, be patient and persistant.