My iPhone says connect to iTunes but won’t update or restore

On the computer, launch the latest version of iTunes. (If you need to, you can download the latest version of iTunes at https://www.apple.com/itunes )

With the iTunes logo showing on the phone screen, plug the phone into the computer with a genuine Apple lightning cord.

A prompt on the computer screen will offer the option to update or restore. Follow the prompts.

This sounds like a hardware issue but might not be one.

Try restoring using a apple cable, different USB port and testing another computer under a different network.