I check the battery already and it 's good. If I wait for a long time like 1 or two hours, I can start it, but if i start, and then off, then start again, it won't work.

There's more here than the alternator. Considering that this isn't a cheap car to mess around with, I would take this in to a mechanic that's familiar with Infiniti or Nissan. It sounds to me like a coolant temperature sensor or something related is malfunctioning.

could be 23435366435 different things its not a cheap car so take it to someone that knows what they are doing...its not worth screwing something up good luck