IPhone 4 is frozen on Apple screen. What do I do?

It's stuck on the screen with the apple.
It's plugged into my computer but it doesn't change.
I can't restore it because I have to have the iTunes screen show that the phone is plugged in.
I've held the sleep/home button down together and it changes the screen to show that the phone needs to be charged.
When I plug it back into the charger, it does the same thing all over again.

Hold the off button for a long time and it shall turn off then turn it back on again.

Bring it to the apple store and see what they could do to fix/resolve the issue. That is the first thing I would try. You could also hold down the power and home button for a moment to see if anything changes, as that could work too.

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