The point is, however, that you cannot vote for a 34-year old, or even a 35-year old. You would have to vote for electors for some particular individual. If the electors are qualified, but not the candidate, the electors would still be elected. Presumably they would not be allowed to then vote for the ineligible candidate.
My guess is that the electors could vote for an unqualified candidate. After all, they don't HAVE to vote for anyone, as we saw in DC in 2000.
Then, if no
qualified canidate has 270 electoral votes, the election would be thrown into the House, where the House would have to choose among the top 3 qualified candidates. The House would have to pick a qualified President.
But if anything like this ever happened, it would invariably be put up to the courts to sort out.