hey guys, i found the solution for the blank screen probelm for the updates screen. as many of you, i had the same problem on my iphone 4, IOS 6.1.2. so i called the tech support. what they told me to do worked right away.
here is what i did:
1. press the home and power button at the same time (just like taking the screenshot) for about 10 seconds, untill the screen goes dark.
2. ideally, the screen goes dark, and it should come back on in about 10 seconds.
3. if it doesnt, just press the power button to turn it back on.
check the updates screen, and it should work. the techsupport told me it was a 'reboot' function, which just clears some things.....i am not really sure what it is.
so, this is the solution that worked for me, and now it is working properly.
hope this works for you.