iPad 3 stuck in recovery mode
This may pull you out of recovery, but it will clean wipe the iPad. Download the Latest ipsw supported by your iPad. Put the iPad into DFU mode. Open iTunes and press the restore button holding the option + Restore if on a mac, or Shift + Restore if on PC and select the downloaded ipsw file.

P.S: Try this for recovery, it is a paid software. I haven't tried this personally, but the software description says that it can recover data from an iDevice stuck in recovery