Q: Unresponsive Apple Help

If apple knows screens can become unresponsive and make phones unusable, they should have more ways to contact than just with the phone. I have spent a very long time trying to figure out how to get the serial number or email them but cannot do either. They need to have an email for people who are unable to make it to an apple store at the time and whose phone screens are unresponsive. Being unable to contact support when I have a problem with their product is not very comforting.