PaulRB:
Or... the problem could be that the Nano's pins are damaged by sourcing or sinking too much current, what with no current limiting resistors and no transistors or buffer chips to deal with all that current... Depending how they have been abused, they could be low when they have been set to high, or vice-versa, or... But the OP is studiously ignoring these criticisms!
Go blame the guy who put that tutorial on the official arduino website.
Though if the board had been damaged, it would have occured at the very beginning, before I even posted here. Your snide comment about how I am going to destroy the arduino without any explanation is by far the least productive thing in this entire thread. How about you come off your high horse and talk eye-to-eye with a puny uninformed peasant like myself?