Thanks Mr Mind ster i got the problem solved through the following:
I was forced to conclude that the problem must be with the Reminders database, which is stored within the main Outlook database. A web search for fixing the Reminders database did not yield anything useful, other than the tip about starting Outlook with the /cleanreminders flag, which we had tried already with no success.
The user was using Outlook in POP mode, so all mail was being delivered to the *.pst file, i.e. there was no *.ost file. The thing we tried was to replace the *.pst file (named outlook.pst) with a new copy.
The following steps solved the problem:
o Quit Outlook and made a copy of all files in C:\Documents and Settings\<username>\Local Settings\Application Data\Microsoft\Outlook to another location for safekeeping.
o Created a new Outlook data file and named it outlook1.pst
o Made the new data file the default for mail delivery by seleting "Tools -> Account Settings -> Data Files" clicking on the new file to select it, then clicking on the "Set as Default" icon in the toolbar.
o Copied mailboxes from old data file to the new one. We did this in Outlook, by using the right-mouse button to drag folders from the old data file to new. The new file contained an Inbox already, and that could not be dragged over, so we opened the old Inbox, pressed CTRL-A to select all messages, then "Edit -> Copy", then opened the Inbox in the new data file, and "Edit -> Paste" copied all messages to the new Inbox.
o The Calendar and Contacts databases had not yet been moved, but we decided to try a test. We created a new test appointment about 17 minutes in the future, and waited. About 2 minutes later, the normal reminder dialog (fig. 1) popped up with a beep!
o We next copied the Calendar and Contacts list over in a way similar to how we moved the Inbox. First we selected Calendar, then clicked on View -> Current View -> All Appointments to display all appointments as a list. Then we were able to press CTRL-A to select all appointments and copy them to the new data file in a way similar to the Inbox. For Contacts, it was similar except we selected View -> Current View -> Phone List.
o After some testing to be sure that all was working, we simply deleted the old outlook.pst file.
Problem solved. The reminders and all other features have been working fine since then.