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I tried having odin open on the pc while i booted into download mode. Removed battery and usb cable from the phone, inserted battery while holding vol down and home. Download mode came up, pressed up to enter and quickly inserted the USB cable. Odin detected the phone and one second later shows it was removed. I have tried multiple USB cables as well.
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After several hours of cussing and google searching I came across a thread that described my issue perfectly. The solution turned out to be a stuck power button on the phone. Just like my phone, the one in the thread would boot immediately when the battery was inserted and shut off at the splash screen. Recovery and download mode both did the same, as does my phone. The site suggested rapidly tapping the power button to jar it loose. This did not work for me. Neither did the suggestion of sliding a finger nail into the gap between the chassis and power button. I went so far as to disassemble the phone and remove the physical button from the case. I put the battery back in and the phone booted immediately. The problem persists, the phone shuts off completely after a 2 - 3 seconds. This occurs with the battery in or with the battery out on USB power.