The answer to no birth or death certificate is generally simple. The State of Illinois did not MANDATE such records prior to 1916. After that it is a bigger issue and the subject of a different post.
Marriage records were always required and yet many times they cannot be located.
Obviously, they may not have gotten married where you think they got married. For Illinois marriages prior to 1900 researchers are in luck. The State Archives database, online, free and searchable, lists most marriages prior to 1900. You do not have to know the exact year. You can search by bride or groom's name, then by county or statewide.
Start your search here: http://www.ilsos.gov/GenealogyMWeb/marrsrch.html
The State Archives volunteers are working on 1900-1915.
My great grandparents have no marriage record in Illinois. I have searched statewide by their real names and assorted different spellings. I have been to the county courthouse in the county where one would assume they married and checked the county courthouse where his obit says they married. There were no courthouse fires between then and now.
Their first child was born more than nine months after the marriage, almost two years before if you believe the one census that lists it, the 1890 census being lost. [I don't.] I can think of no reason to hide or otherwise destroy the record.
They married in the winter, Valentine's Day. There is a formal portrait of the couple, probably not taken on the wedding day but undoubtedly shortly thereafter, before her first pregnancy was visible.
Less than 20 years later he was dead and she was left with four sons. There are court records certifying her as the widow. So where the heck is that marriage certificate?
Perhaps the minister lost the return before he had a chance to turn it in. Perhaps the clerk lost it. Perhaps it was lost sometime in the next 100 years that passed before anyone noticed it could not be found. Maybe
This is one of those mysteries I don't think we will ever solve.