laexel,
It was not clear from your original post if you actually deleted your "My Card."
Before deleting the card, make sure iCal is not running. Then delete the com.apple.ical.plist file. You will find the com.apple.iCal.plist file in your Macintosh HD/Users/yourusername/Library/Preferences Folder. Drag the com.apple.iCal.plist file to your Desktop, log out/in or restart. Next delete/recreate/designate your "My Card" in Address Book, and see what happens when you open iCal and set an alarm.
;~)