Hi Randy Zeitman,
Welcome back to Apple Support Communities. I understand that you're currently having an issue with your alarm clock and not being able to delete any alarms, I certainly understand how important it is to have a working alarm clock and would be more than happy to help get this resolved.
Check out this article with steps to Force an app to close on your iPhone, iPad, or iPod touch. This will allow you to close the app you're having issues with.
Then go back into the app and try to completely delete any and all alarms once more that are currently saved and then close the app again. Next, check out this article with steps to Restart your iPhone, iPad, or iPod touch.
If that doesn't work, it would be a good idea to be sure there is not a software issue as the root cause of this for you.
- Check out this article for the steps for How to backup your iPhone, iPad, and iPod touch.
- Use this article for the steps to Use iTunes on your Mac or PC to restore your iPhone, iPad, or iPod to factory settings.
- Once that is done, set the phone up as new and test the phone to see if the issue is still going on. Then, follow this article to Restore your iPhone, iPad, or iPod touch from a backup
Please feel free to let us know if this helps or if you have any further questions.
Cheers!