As others have suggested, you want to be sure and check the battery first. With high humidity, it's likely you just have dirty terminals. One way to normally check for dirty battery terminals is to turn your headlights on. If the terminals are really dirty, the lights won't even glow. If they come on, hit the starter switch. If they go out instead of just get dim when you hit the starter, you know it's dirty terminals. If you have a voltmeter you can check the battery charge by looking for 13.5 volts or more.
There are many things to check, but when I hear a clicking sound, I start looking at the battery really quick.