Refuses to turn on even with full battery

1) power button does not turn phone one

2) Plugging charging cord into phone starts boot up process but quickly turns off and reboots(repeats infinite)

3) Holding the volume up or down while plugging the phone in puts the phone is download mode/odin mode

4) Pushing/holding the power button has no effect on device

samsung refused to warrantly the phone due to a thermal crack in the screen that they faulted to damage.

I can get it into download mode and have tried flashing a new clean stock rom. Does this sound like a motherboard problem or a charging board assembly?

I found this part: http://www.etradesupply.com/oem-samsung-...

but cannot find a place to buy the motherboard for my S4 I545 (verizon).

What options do I have to repair this(other than the $70 replacement fee samsung wants to charge)?

Thanks guys.