Does anyone know why the App Store won't open

I'm not sure your problem, but an easy attempt for a solution if you have not already tried is (1) closing all of the apps on your device, and (2) holding down the power and home button simultaneously until it shuts off. If you are using an iPod or/and iPhone of course. Otherwise with no other information I don't know.

Hi

Go to itunes main page bottom of page sign out

Then sign back in.

Also try the reboot again but hold both buttons for upto 30seconds

Or until you see Apple Logo .

Cheers

Brian