You can try removing the plist files. Please note this may delete certain settings you had in iCal and you will need to adjust them again. Back up your calendars, if they are stored locally (stored on your machine as opposed to Google, iCloud, etc.)
- Open Finder and hit Command+Shift+G. Here type in the following location: /Users/YourNameHere/Library/Preferences
- This will take you to the Library folder, which was hidden in Lion. There you will find about 4-6 files that have iCal in the name. (ex: com.apple.iCal.plist)
- Take these files and move them to a different folder temporarily. There should be no iCal plist files left now.
- Procede to restart you computer with the box for "reopen windows when logging back in" unchecked. After the restart, open iCal and allow a moment for iCal to rebuild it's plist files. If iCal ceases to work after this step, just replace the plist files you moved temporarily (shouldn't be an issue though, I wrote this just in case).
Theoretically, most applications can rebuild their plist files and go on without a problem. If this doesn't work, there could be an issue with a sync service that will take a much more to fix.
Let us know if this fixes the problem. Good luck!