iPhone 5 won't start after an iTunes recovery I shut down my iPhone 5 phone in the middle of an iTunes purchase download. 

I went to an At&amp;T store and they reset the phone. After three hours the phone went blue.  Phone will not turn back on now after doing the recovery via iTunes on the computer. The download did complete. At this point I can get the apple logo to show but that is all.
Force it into Recovery Mode, then restore... 


Switch off the device &amp; leave it off.
Connect the USB cable to a computer with iTunes [ideally one that has been used with the device previously]
Whilst holding down the Home button, connect the device to the computer [keep holding Home until you see the 'connect to iTunes' screen.
iTunes should launch &amp; detect the device is in Recovery Mode.
Use iTunes to restore.


Ref: If you can't update or restore your iPhone, iPad, or iPod touch