There should be a record of her voting then in both counties. That needs to be checked out. If found to be true, that should be enough for Thune to go ahead with a contest.
It looks like the county registrar was the one who discovered the duplicate applications of the dead person. If that is the case and the case of other such frauds, then there is a good chance that no ballots were sent to the fraudulent parties and these fraudulent votes were not cast. That would explain the lack of action on the matter.
Looking at the situation in SD and the overwhelming Republican support in other offices, I wonder if these Democrat senators EVER really won office?