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There are two possibilities that I can think of:
1) when you set user permissions, you (logically) went to the permissions page, clicked the appropriate check-boxes, and hit "submit" at the bottom of the page. It took me a little while to discover that to set each group of permissions (View, Submit, and Auto-Approve), you must clicked the appropriate check-boxes in the top group's box, then click the submit button under that box, and wait for the page to reload before scrolling down and setting permissions for the next group, and then follow that routine again for the last group of permission. If you try to fill them all out at once, only the last group of permissions (Auto-Approve) is enabled.
If you already figured that out and this was not the problem, I would then ask if you are using the default theme. If you are using the default theme, immediately after you select eXTCal from the main menu, a "Submit Event" button should pop up underneath the main eXTCal button. I can't remember which theme it was, but there was one I tried that didn't handle the sub-item buttons correctly.
One thing that I did, because so many users didn't see that a "submit" button popped up, was to add a link to the submit page in the template file: extcal_calendar.html
But let me know if either of the first two options applied.
Improve the time.