Had they not cheated in 1960, John Kennedy might have lived into his 90’s+
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JFK would have won the election without Illinois’ electoral votes:
Kennedy 303, Nixon 219, Harry F. Byrd 15.
Kennedy still wins even if you take his 27 Illinois electoral votes and give them to Nixon.
I think the cheating was about the North Carolina primary, which was close and he needed to win the primary in order to be a candidate.
You are correct. They were possible claims of fraud in both Illinois and Texas. So Illinois could not have done it by itself. Total electoral votes in both states was 51.