Not sure where my key is,
Aperture 3 displays the registration key in the "About" panel: In the main menu bar: Aperture > About Aperture.
Make a copy of the registration number you are seing there and keep it save.
What is your Aperture version? If it is not the current Aperture 3.5 and licenced to the AppStore, you cannot download it any longer from Apple's web site. You will need to find your installer disks as well, to be able to reinstall Aperture.
Reinstalling Aperture will only help with your kernel panics, if a faulty Aperture installation is the problem.
Other applications hat you installed recently may cause Aperture to crash and the system to panic as well. Have you tried to remember, what else you installed recently? Any plug-ins for Aperture, any other recent third-party applications that may need upgrading? Any helper tools for monitoring the system, cleaning the system, additional fonts, etc?