Do you have an immigration date for him? Can you attach an image of the ship's manifest? (I suspect they were before 1884, and those images are not much help, but seeing who they travelled with might be.) Since he was in Chicago, do you know which church they belonged to? If their daughter was baptized in a Catholic church in Chicago, chances are very good that you can get a record. Some of them listed the villages of the parents. Of course, if you have gone down all those avenues already, it's a good idea to say in your post that they didn't lead anywhere.
All the Tichaceks I know are from Moravia. My Srameks are from Bohemia, but about 10 miles from the Moravian border. As Jean suggested, break each of these out into separate threads, one person each, or if they were a married couple when they immigrated, then the two of them in one post, because they probably came from the same area. Birthdates if you know them. Any old letters or anything written in Czech? You never know.
Mary Sramek Levesque