This is an archaic use of language that's confusing even for native speakers. 'Would' here means 'wish' or 'desire'. Take out the money line and the sentence is a bit clearer.
"I wish not that the cardinal had died."
Or to put the words in a more conventional order:
"I wish that the cardinal had not died."
The money part is emphasizing how much he wishes that the cardinal hadn't died. Not even twenty thousand pounds (a vast sum at the time, as the next few paragraphs makes clear) could change the king's mind about wishing the cardinal hadn't died.
In more modern language the sentence could be written:
"I wouldn't wish for the cardinal to have died, not even for twenty
Why that particular sum of money, I couldn't say, as that probably strays more into literary criticism or Tudor economics than English language.