As long as you have eagle.key, you don't need the original registration file and activation code.
Hmmph. I do have an "EAGLE.key" in the bin directory, but it's apparently not accepting it.
I wonder if some of the pathname changes that occurred have gotten in the way (It's a Mac.)
I tried to recreate copying the eagle install directory as I said, and now I can't get it to work. There are other differences involved, such as the Linux distribution, so it could be that. But it seems more likely that I must have re-entered the license years ago and forgotten I did that. I apologize for steering you wrong.
I tried a few things to get a copy to run like changing the MAC address and hostid on the target host but that doesn't seem to be it (or at least not all that it wants).
One thing I can say is that eagle.key is invalid if the eagle executable is moved to a different partition and a symbolic link is left in its place. This is on a host where eagle runs fine. So, maybe something about the physical disk? It also won't run using a double symbolic link pointing to a link on a different partition which then points back to the original executable, which I didn't expect, but there could be an explicit check for this.
Mounting an old system's disk on a new system with the old eagle installation directory, including the old eagle.key that was installed with that system, surprisingly works when executing out of the old directory. And changing the UUID of the old system partition doesn't seem to bother it; it still runs.
Maybe some sleuthing with strace can figure out what eagle is looking at. Some cursory runs with strace says it does retrieve the ethernet mac address, but that's only in the case where it's about to fail. Perhaps it does some quick checks for license/platform validity, and then if something seems fishy, starts to dig deeper.
And this is experimenting with linux. It could be different with MacOS.