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I wonder if they checked alternative spellings? That is a common reason that a birth record isn't found when you know the date and place for a fact. There can't have been that many births in Lincoln Co., WI in 1926. Sometimes it helps to just look for a first name (and I would try Hildegard as well as Hilda). However, most civil servants aren't willing to do this. You would need to check the records yourself.
Is there a remote possibility that she was born in a nearby county? OR perhaps a year close to 1926?
The Wisconsin state library may also have microfilms of the Lincoln County records.
Another possibility is to try the Wisconsin Department of Vital Records and have them do the search for you. They will do a 5-year search in case the year of birth is wrong. That happens more often than you might think.
And sometimes we face the sad prospect that there is no birth record - for whatever reason. Sometimes this is a family failure to register a birth. If she had siblings, have their birth records been discovered?
I have found no birth records in any database online for Hilda in 1926 +/- 5 years in Wisconsin. Of course not all state records have been transcribed and made available to the public. When that happens one has to go to the source.
Please let me know what additional questions you may have about this.
Did you have additional questions about this? If not, I would appreciate a rating (hopefully a "5") since that's the only way I'm paid for my time.
I can't afford to go to Wisconsin to look for one for you either. I have to work, looking for information for descendants. When I don't get a great rating, I'm not paid for my time.
As I mentioned, the Wisconsin Department of Vital Records will do a 5-year search in case the year of birth is wrong. That happens more often than you might think. People fib about their ages for all kinds of reasons.