What is the minimum depth for fence post holes in Illinois?

Your frost line is about 42 " but it really depends on what kind of fence you will install and will it be supported with concrete. For most residential privacy fences in Illinois I'd go with 36" but tell us about your fence.

Metal posts, wood posts, are they going to be set in concrete. What type of fence is it for.

Yes the corner posts should be a little deeper or the posts you want to swing a gate from. Going below frostline insures the posts won't tilt or heave out.

Your frost line is about 42 " but it really depends on what kind of fence you will install and will it be supported with concrete. For most residential privacy fences in Illinois I'd go with 36" but tell us about your fence.

It's a vinyl fence and it's 6 feet. Post are 5x5 rather than traditional 4x4. The post will be set in concrete. All corner posts and gate posts will have a secured 4x4 wood post inside the 5x5 vinly post.

I would go to a 48" deep hole with this installation. You hole should also be at least 12" in diameter. Illinois frost line was shallow this year due to the heavy snow but if frost gets beneath a concrete post it will raise/tilt the entire block of concrete.

What is the minimum depth for fence post holes in Illinois?
1/4 of post height should be in ground. Hole should be not much larger than the post size. Pack-in around post solidly. Frost should lift all posts evenly, and they should settle down in the spring.

Not sure where you heard 1/4 the post height but that is not correct. Think about it, a 4' tall fence would only be 1' in the ground. This is wrong, as is your assumption that frost will raise things evenly and then settle evenly in the spring. I don't know how much frost your folks get in NC but Illinois frost can lift a house or garage.

6" below frost line is really the best, ballenger is giving you good advice (as usual), I'd go with what he says. The manufacturer of your fence posts should have some instructions as well.

Not sure where you heard 1/4 the post height but that is not correct. Think about it, a 4' tall fence would only be 1' in the ground. This is wrong, as is your assumption that frost will raise things evenly and then settle evenly in the spring. I don't know how much frost your folks get in NC but Illinois frost can lift a house or garage.
Yes, the frost line is greater in Illinois, but whatever rises will fall to its rested state after the thaw. If you want to go three feet into the ground or just past the frost line it will indeed snap off when a car hits it, rather than lay down to be put up again, without having to purchase a new post. Al things considered.