IPhone – My iPhone will not turn on. Please give me advice

I'm afraid you've busted your iPhone. There's no easy solution.

That power button is known to be a weak spot, and submitting the phone to excess humidity (or direct moisture) is never a good idea, even if you weren't planning to be in that storm.

From your description it sounds like the switch is slowly corroding. It will not get better, only worse over time. I'd suggest to have the phone serviced as long as it's otherwise still in good condition, or give up and replace it sooner than planned.

You could also try to repair it yourself by opening it up and cleaning that switch, but it might not even be possible, and worse: you risk breaking your phone. Have it serviced instead.

No, the iPhone does not self-condition. Apple has a guide for conditioning laptop batteries, yet I can't find a version for iOS devices (still looking).

There is a general tips page on maintaining great battery life, as well as general terms about battery replacement.

Personally: This sounds like a bad battery. It sounds like it just plainly is not holding a charge after a certain discharge point. Remember that iOS multitasking is not true multitasking. Barring streaming audio (actually persistent audio in general), there is (almost) NOTHING that your phone can constantly do for more than 20 minutes at a time.

I've streamed audio for hours (hours being... maybe 5?) during the day at ~40% and it did get under 20% by the time I was done, this was both on an iPad, and roughly equivalent on an iPhone 4. Connected WiFi, 3G (on the iPhone) enabled but not being the active radio in use, of course.