The XSKey *needs* to be physically connected to your computer when installing the update version of Logic 8, there's no way around it. Once you run it for the first time, you can disconnect the key and store it at some safe place, Logic will never ask for it again.
With a broken key, you better make sure to find it. Perhaps you can talk to Apples support and when you send in the broken key, they might send you a full version of Logic 8 rather than an update (the full version doesn't need any key at all).
You may as well try to copy your existing (and still intact, as you say) Logic installation to your new machine (just make sure to also copy the preference files related to Logic). No idea whether that'd work, but it's perhaps worth a try.
Or you could perhaps even check whether the migration assistent (I never actually used it myself) allows for the transfer of single applications and their settings.
- Sascha