Since, as you said yourself, the airport WAS working before installing FSUIPC, I can't see how you can blame the airport about this problem.
If the Addon Manager says the airport is active, then IT IS active so, your problem doesn't have anything to do with activation or registration.
As was explained, many times already, in any case you lose your activation, for ANY reason: first, the Addon Manager will not report the scenery as "Active" anymore AND, more importanly, IT WILL NOT JUST DISAPPEAR! It will simply run perfectly, with all buildings, just for 5 minutes at a time. And, of course, there will be a clear indication of the scenery being in Trial, because you'll see a green text line stating the Trial has begun, each time you go to the airport.
If, instead, you just don't see the scenery right from the start, with the Addon Manager reporting it as Active, it's not an activation problem and, if you DO see the Addon Manager (which you surely do, otherwise you wouldn't be able to check that is saying "Active" ), then it means the software is also running correctly.
If it doesn't show up, it's either a problem created in some way by FSUIPC ( although, as I've said already, I've tested it with the latest version and it works just fine ), or another entirely different problem.
For example, something that might result in the airport not displaying, it's a double entry for it in the Scenery Library. Or, having moved away from the topmost position ( or, at least, on top of anything that might exclude it ).
About installing: it's best if you do it with an internet connection available, because the installer gets the very latest version of the Addon Manager .DLL online. However, the one that is included in the KLAX installer should work in any case, just it might not be the very latest.
But in this case, if you don't have a connection when installing, it's best to Uninstall by replying YES to the question "Do you want to remove the Addon Manager?"