Hello Patty1959-2013,
Thanks for reaching out in Apple Support Communities! We understand your concern with the way the MacBook Air is booting up. Also iTunes makes the dinging sound. We're happy to assist you with this.
Let's start by booting your Mac in safe mode. Safe mode can resolve many issues like the ones you're having: How to use safe mode on your Mac - Apple Support
While in safe mode, test to see if the same issue occurs with iTunes.
Make sure there are no updates for your Mac:
Update macOS on Mac - Apple Support
Take a look at the images in this article to see if any one of them are the screen you were seeing when your Mac boots up. This will provide a better understanding of what's going on:
If your Mac doesn't start up all the way
Thanks for using the Apple Support Communities, and have a great day!