Where can I find my activation key?

If you updated to the Mac App Store license when you installed Mavericks (which its seems you did) you can just download Aperture from the MAS after you do the reinstall of Mavericks, no need to mess around with local copies. You;re more likely to get a good install this way.

Just log into the MAS using the same Apple ID you used when you upgraded Aperture to 3.5.1

regards

Which Aperture version are you currently running, Nicolas?

If it is not an AppStore version, you need the installer DVD to reinstall. The earlier Aperture versions are best installed and not migrated.

As to the registration key:

Earlier Aperture versions up to version Aperture 3.4.5 will show the registration key in the "About" panel - in the main menu bar: Aperture > About Aperture.

(added: It will only show the last registration key. If you have an upgrade key, you will need the keys of the previous versions as well).

If you already updated to Aperture 3.5.1, you do not need your Aperture serial number any longer. Aperture will have been associated with your Apple ID and it will show on the "Purchases" tab of the App Store, when you sign into the Store menu with the Apple ID, that you used, when you updated Aperture. Check the App Store and the Purchases, before you wipe your drive. I strongly recommend to update to Aperture 3.5.1 and to associate Aperture with your AppleID, if you have not yet done that. Then you should be able to reinstall from the AppleStore. But keep a backup copy of Aperture 3.5.1 just in case, since the current version at the AppStore is Aperture 3.6, that will require Yosemite.

As long as Aperture is running find the serial number by doing Aperture->About Aperture

If it is not running there is no way to get it from the software.

regards