EXACT same problem here. bradley. when you say "recovery mode", do you mean that you get a screen that has an image of cable and a url a top that says something like "www.apple.com/support"? sure i've got this....while plugged into the wall connector, but immediately after i unplug to transfer to computer the phone powers off. useless.
i was told the phone was 'dropped' hmmm...now the phone just goes through a continuous loop of of apple logo, black screen, and sometimes a flash of a solid red screen.
the phone will not loop if connected to computer through usb...it just basically is dead. well sometimes it will give a glimmer of hope when connected to computer, such as going through the logo, black screen sequence once, but immediately shuts down.
basically it will not power up unless directly connected to a wall charger. none of the recovery boot up sequencing has been successful...and i've tried them all, multiple times. believe me, i have.
i'm guessing the it could be a battery issue, or circuitry. seems like my software troubleshooting is not working, so time to investigate hardware issues.
what tools do i need to crack this little open?