Default [Q] Phone Crashing Out of Download mode and Recovery mode

Hello all,

My phone randomly got stuck in a boot loop (crashing after the black and white galaxy s3 splash screen) last night and is now on its last leg. I'm on stock ATT firmware; I had messed around with rooting a few months back but restored.

Now the phone will crash before entering recovery mode. I can get into Download mode and connect the phone to ODIN, but it will crash before it can begin rewriting the firmware. The phone just won't stay on for longer than ~20 seconds (I've tried with two different batteries). All I can figure is that there is a hardware power issue, but do you all have any ideas? If not, I fear I'll have to buy a new phone.

PS: I initially believed the power button was stuck and opened the phone up to make sure that wasn't the case, it was fine.