Bill Cameron
Banned
Hamilton was ineligible for the presidency.
Article 2 Section 1 of the Constitution of the United States of America
No person except a natural born Citizen, or a Citizen of the United States, at the time of the Adoption of this Constitution, shall be eligible to the Office of President; neither shall any Person be eligible to that Office who shall not have attained to the Age of thirty-five Years, and been fourteen Years a Resident within the United States.
As others pointed out before your post, Hamilton is most certainly eligible for the Presidency. In fact, the phrase "or a Citizen of the United States, at the time of the Adoption of this Constitution" was most likely added so that Hamilton could run for the Presidency if he wished.
Which really is a good thing, in my opinion.
Sadly, the worth of your opinion is mitigated by the fact that you weren't aware of what the Constitution actually says on the matter.
Bill