Earlier this morning I tried connecting my iphone to my windows PC but I keep getting this message “iTunes could not connect to iphone insert device name because the device timed out”. I tried restarting my phone, restarting the pc and it still didn’t work. Luckily, I was able to find this post. The solution was:
Hard reset your iphone or ipad!
To do this just press the Lock and Home button for a couple of seconds until the screen goes dark and wait for it to boot up.
It worked for me so I hope it works for you too!