iPhone 3GS won't turn on or reset, what could be wrong?

I was in the middle of a call on my iPhone 3GS when it suddenly turned off. It might've been because the battery ran out of juice, but I don't think so. I went home and tried plugging in it and it wouldn't charge. I tried both through my laptop and with a wall charger. I even left it plugged into the wall overnight, but all I get is a black screen looking back at me.

I've also tried to reset it and put it into DFU mode, but no go. I can't get the Apple logo to appear, nor can I get the laptop or iTunes to recognize the phone. And yes, I have tried to reset it while having it plugged in.

I've had no previous problems with the phone, aside from the vibrate switch wearing out. I did update the iPhone to 6.1.3 from 5.1.1 two days before this happened. I bought the phone used off eBay about a year ago. To me, it seemed like my iPhone's battery might be dying kind of quickly. It would die in about 12 hours and in much less time if I was using it. The Apple Genius pretty much told me he can't tell what's wrong and I'm !@#$-out-of-luck and offered a replacement for $150.

Anyway, I'd like to repair the phone myself, but I'm not sure what's wrong with it. My inclination is to suspect the battery, but I'm just not sure and thought to bring my problem before those much wiser than I.

tl;dr I was making a call on my iPhone, halfway through it shut off and now I can't get it to turn back on. No previous problems.