Yet another wet iPhone...but it sorta works

As I read these threads I always wonder...what kind of idiot drops their phone in water??? Sure enough, as I'm on vacation with the iPhone on top of my towel next to the hot tub, like an idiot, I yank the towel to dry off and plop goes the phone in the tub. I quickly went to grab it and tried to shut it off, and I did. Unfortunately it kept turning on and off by itself (apple logo on and off). Since I was on vacation, I didn't have tools to open it, so I had no choice but to let it run out of juice.

I asked the hotel for some rice and put it in a ziplock bag. Waited 3 days and turned it on. Good news is it turned on and asked if I wanted to restore. Bad news is it's showing as 7.1gb (out of 16gb), the screen is faded, and the phone when not connected to a power source for a few minutes, reverts back to the apple logo on/off behavior, also the volume up/down and top button don't work.

I decide to put it in rice and a few desiccant packages for 2 more days. I take it out and now the screen is back to normal. But the other problems still persist. I can deal with half the storage. I can even deal with broken buttons. But I need this thing to stay on for more than 5 minutes when not plugged in. Any ideas other than I'm SOL? And yes, it's well out of warranty. I think I'll put it back in the rice again and hope for the best.

Thanks!