Hey there, acorbett,
Thanks so much for using Apple Support Communities.
We can absolutely help you get Mail working with your Yahoo account. Rebooting was definitely a great first step. Another good step to start with is making sure that your iPhone is running the latest version of iOS, since those updates can often include resolutions for this type of unexpected behavior. This article goes over how to update: Update your iPhone or iPad - Apple Support.
If the issue continues to occur after updating, can you try adding the account as "Other" instead of Yahoo during the initial account setup process and see if that works? This could be a temporary workaround and might cause issues with things like Contacts or Calendar but we want to see if it may resolve this now so that you can get that account added to your device.
You can verify if your email settings are correct using the "Mail Settings Lookup" tool on this page:
Mail - Official Apple Support
We hope this does the trick for you!
Cheers.