Q: how to turn my ipone 4 on.

Hello bascartoon3,

Thank you for posting in the Apple Support Communities.  It sounds like your iPhone is prompting you to connect your iPhone to iTunes, but your iPhone is not visible in iTunes once you connect it.  It is certainly impossible to use your iPhone when it's in this state, but I did find some steps you can follow that should help with this:

iPhone not appearing in iTunes

http://www.apple.com/support/iphone/assistant/itunes/

I recommend following the steps in this tutorial in order.  You can skip any steps that are not relevant or you have already tried.  I hope this helps!

Best,

Sheila M.