iPhone 4 will not turn off

You may have an app running.

Try force quitting.

Force quit an app: Press and hold the On/Off Sleep/Wake button for a few seconds until a red slider appears, then press and hold the Home button until the app quits. You can also force an app to quit by removing it from the recents list.

See “Opening and Switching Apps” on page 29.

From the iPhone user guide: http://manuals.info.apple.com/en_US/iphone_user_guide.pdf

What happens with you tap & hold the sleep/wake button? Does the slide to power off appear? If it does, what happens when you slide to power off?

What happens when you "Slide to power off"? Does the spinning wheel just keep spinning and never go away?

Try resetting your iPhone by pressing the home and sleep buttons until you see the Apple logo, ignoring the slider. Takes about 5-15 secs of button holding and you won't lose any data or settings.