I'm extremely sorry to learn of the issues you may be having with iTunes. We certainly want to make sure all software you utilize is functional. Since iTunes is an Apple product, I do recommend reaching out to Apple for assistance with their software installed on your computer. Their contact number would be 1-800-MYAPPLE (692-7753), thanks!
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Quick fix, remove iTunes from your computer and then reinstall the newest version I think its 11.5
However in itunes you can click Help-Check for update and that will update your itunes on the computer.
Then plug in the usb cable from the phone to the computer and itunes should open up.
itunes also can sync via wifi if that setting is set on.
If its iTunes on your iphone, well Verizons answer is correct contact Apple http://www.apple.com and search the forums or call them. Please note calling may incur spending money for the support.