iOS 8.4 update won't install, just hangs on "update requested".

I think we experienced the same problem. I tried to update to iOS 8.4, and it failed. Then, my phone became locked on the "update requested" screen. I couldn't connect to itunes afterwards, even after powering the phone on and off. It was basically unusable.

So, I took it to the Apple store, and here is what the tech did. He put the phone in "recovery" mode by holding the home and power button down at the same time for about 5 seconds. Then he let go of the power button, and he kept pressing the home button down for another 5 seconds. The internet may provide better instructions for doing this. After the phone was put into "recovery" mode, he connected it to itunes, and the phone was "restored." However this will erase all your data on the phone. If you try this, hopefully you have backed up your phone on itunes or some other software.

Hope this helps

If you can't update or restore your iPhone, iPad, or iPod touch - Apple Support