iCal/Calendar.app tends to not like syncing by both iCloud & iTunes.
I suggest you look here: http://support.apple.com/kb/ts3999
Have you tried turning calendar syncing off in System Preferences?
I'm sure, like me, you are baffled.
In Itunes I have it set for syncing when the iPad and iphone is connected or via wi-fi.
Calendar on iPhone 5 and iPad is set for Events 1 month back. The iPhone 3GS has all the syncing shut off (mail, calendar, etc).
I shut off the iCloud syncing, but that didn't do anything. Restarted the iMac as well.
Not sure what the issue is as obviously Calendar is running that the date is always updated and the menu bar appears etc. it's just that I can't see the actual calendar on the iMac.
Maybe in time it will work itself out? LOL!!!!
If you turned off the iCloud syncing after doing the Calendar folder Time Machine restore I would try the 'restore' again. If the calendar stays visible long enough make a backup of each calendar.
To do that, select each calendar in turn and from the File menu select Export... > Export...
If you can save the calendar data it should be possible to clear the application's user data and start again.
The application works ok in a new user account. So, the problem is with your user data.
To completely remove the calendar data for your User account go to the User's Library > Calendar folder (as above) and remove the entire contents of that folder. Then start the Calendar.app. You should get the default empty 'Home' and 'Work' calendars.
it is possible re-syncing to iCloud after this will return most of your events.
I went in and deleted all the files in the User Library > Calendar folder. I tried restarting the Calendar and got the same results before (bouncing icon and menu bar with drop down menus). I then tried deleting the files from the folder, and then tried deleting them from trash. Even with the calendar app closed (quit calendar, and also tried forced quit of calendar), when I go to delete the trash I get the notice, "The operation can't be completed because the item "Calendar Cache" is in use.