Based on sources such as Chicago Tribune, Encyclopedia Britannica, Slate Magazine and many other books, it is said that JFK's father played a significant part in making him president. In the book, "If It's Not Close They Can't Cheat," by Hugh Hewitt (page 60-61), it is claimed that JFK's father "helped" him illegally become president. What is some of the proof for and against this?
As per your original question:
The Wikipedia section does not claim that Joseph P Kennedy bought John F Kennedy's victory. Such claims would be rather outlandish as it would mean that he was the only or the major contributor to the primary election campaign. As JFK would not have been able to win the democratic primary election unless he had widespread support within the Democratic party, it is unlikely that he couldn't find campaign funds from many other sources.
As per your updated question:
There have been investigations and recounts into this election, none of which found any voter fraud. The claim of voter fraud is just sour grapes from Republicans, just as with the claims of voter fraud against Bush.
About Joe Kennedy's influence on making JFK president:
Joseph P Kennedy was involved in politics, and knew a lot about politics, and helped out his son in his political career in many ways. I don't see how this is strange or controversial in any way. And it doesn't mean he paid for the presidency.