System Preferences-->iCloud-->Sign Out doesn't work? Are you able to select/deselect different iCloud services?
If that is the case, I suspect you'll need to open a terminal window and delete (or safer, move) the ~/Library/Application Support/iCloud folder and then set up iCloud fresh. I have not tested this procedure so YMMV. That is why moving the folder would be safer so you can put it back if it makes things works.
You also may try deleting ~/Library/Caches. Deleted caches is generally safe and can generally only help issues.
Have you tried looking in console for any error messages?
Nope, systemù preferences doesn't work.... it asks me about losing information and then nothing happens
Hmmm, I'm certainly not an expert user.... you already lost me at "terminal" and deleting things sounds like a recipe for disaster!
I was rather hoping for a way to re-install and be back up and running!
If you're able to get into the calendar now, use File-->Export to back up your calendar data.
When you get to the point of system preferences-->iCloud-->Sign Out asking you to delete the data, you'll need to say "yes". Then when you reconnect to iCloud, the system *should* download the calendar info from iCloud. If not, but everything else is working, retrieve the calendar data from your back up.
Have you tried restarting the computer?
If yes, and no change, then I would proceed with reseting sync history or http://support.apple.com/kb/TS2481?viewlocale=en_US&locale=en_US (if Mountain Lion or older).
If using Mavericks, I would still be inclined to follow the basic steps in the second article to delete the contents of ~/Library/Caches and the Calendar Cache files in ~/Library/Calendars. Deleting caches is generally safe and often solves problems with applications hanging up.
Go to Finder
While pressing the "option" key, click Go->Library
Then navigate to the Calendars folder and the files starting with "Calendar Cache" to your desktop
Navigate to ~/Library/Caches and select all the files inside that folder. Drag them to your trash.
If these steps do not work, I would probably follow the steps above to go into the Library folder and then move the iCloud folder to your desktop, then restart.
Again, back up anything you can before hand.