I cannot update my iphone to ios 9.3 - when not connected to my PC, iphone shows error message when verifying update - "iOS 9.3 failed verification because you are no longer connected to the internet", even though it is.

When connected to itunes, I get error message - "itunes cannot read the contents of the iphone" with an invitation to restore iphone to factory settings - bad news because this will erase all contacts.
Anyone else experienced this? Any solution?