Hi 16bluebird,
Welcome to the Apple Support Communities!
We are happy to help with the issue you are having with your iPhone and it not ringing or vibrating. Although basic, you could try a restart and see if that helps. You definitely want to make sure you are running the latest version of software. Learn how to Update your iPhone, iPad, or iPod touch here. You might want to turn the silent switch on and then off again, or vice versa.
Does this happen only with phone calls? Does the same thing happen with text messages or alerts like your alarm?
Hope that helps!