The most effective method of keeping most any unwanted animal out of the garden is a good, tight fence. For burrowing animals like the groundhog you will also need to put that fence barrier parallel to the ground out a distance, like 12 inches, to keep them from burrowing under the rest of the fence. I have seen these buggers climb fences although a loose top that causes them to fall back can deter them.
An electric fence, installed so they make contact with the live wire and a grounding wire, can be an effective deterent also.
Illinois, like Michigan, does have a law that prohibits unlicensed people from relocating unwwanted wildlife and the fines, if you are caught transporting wildlife without that license, is steep.

Here is a link that might be useful: Electric Fence

Hi Julianna,

I feel your pain, as these varmits can wreak havoc on a garden in no time flat.

I picked your topic quite self-serving to a large degree, because I own a site dedicated to animal deterrents.

The site is motiondetectorsprinkler.org and we have helped a lot of folks with severe animal problems get back to normal.

The research I did for this came from an actual customer that bought a Scarecrow Motion Detector Sprinkler and wrote a review.

The link should show up for you where you can read it for yourself.

Hope this helps you out
John Thomas

Here is a link that might be useful: Scarecrow Testimonial