Greetings Enio,
You may run into some trouble on this one as I've seen issues jumping calendars from 10.5 to 10.7 without going through 10.6 in between.
Here is what I would try:
- Create a new Admin user account on your computer (http://docs.info.apple.com/article.html?path=Mac/10.7/en/mtusr001.html)
- Go into your backup and copy user/Library/Calendars from a date when you are 100% confident that iCal had the data you want from your old computer to the desktop of your current user account.
- Put that folder in Macintosh HD > Users > Shared
- Log out of your current user (Apple > Log Out)
- Login as the new Admin user you created
- Go to Macintosh HD > Users > Shared and move the Calendars folder to the desktop of this user account.
- Click once on the Calendars folder to highlight it and then go to File > Get Info
- At the very bottom of the info pane click the padlock to unlock and then click the gear and choose "Apply to enclosed"
- Close the info window.
- Hold down the option key on your keyboard and then click on "Go > Library" (Go is at the top of your computer screen)
- Move the existing Calendars folder in this location to the trash.
- Drag the Calendars folder from the desktop into the Library where the original folder was previously.
- Launch iCal and cross your fingers.
If your calendars show up, click on each calendar on the left hand side of iCal one at a time highlighting it's name and then going to File Export > Export and saving the resulting calendar file to the desktop. Once you have them all exported you can put them in Macintosh HD > Users > Shared, log out of this new user account and back into your main account. Drag the files out of Macintosh HD > Users > Shared to your desktop and double-click them to import them one at a time into iCal in your user.
If your calendars do not show up in the new user after taking these steps let us know.
Hope that helps.