I’m sorry to say I didn’t find this fix, I just got so fed up with the problem I’ve been having for the last couple of days that I did a search and turned up this page.
Basically, the problem I was having was that my alarms were going off (they were sounding) but I wasn’t getting a little pop-up tab to dismiss them. Result was that my two morning wake-up alarms were going off and sounding off on top of each other and I had no way to shut the device up except to mute it.
The thread linked to above points to this page at ScaryBear who has a utility called CheckNotifications. I loaded up CheckNotifications (used the CAB version) and it told me that I had 415 notifications in the queue. I got it to delete the duplicates and now everything seems to be working again.