I have an iPhone 4 and it only turns on when plugged in. I dropped it one day and it wouldn't turn back on. I know for sure it's not stuck in DFU mode. When I plug it into my wall charger it will turn on and it will take me to an iOS 6 setup saying slide to setup. I do so and it just says connect to iTunes. I attempt to connect to iTunes and it just flashes on and off. The Apple logo will come and than it will turn off. I called FastFix in the mall and they told me it was probably the battery, But, I'm not paying $50 dollars to have it checked out. That's just the biggest rip off. I'll only pay for a repair. I need an answer. I miss my phone and I want it back. Please only answer if you know what you're talking about. It's not the charger, it's not the port. I just want to know for sure if it's the battery. Thanks.
Added (1). It dies as soon as I unplug it.