Let's take this one step at a time. First create a new username in your Windows with administration rights. You can do this from the Control Panel. Secondly, remove everything related to NC Launcher and Aion (game folder, Gameforge, NC Launcher, custom folders, registry keys). After you have done this, make sure you also have the latest Visual Runtime installed (2008 and 2010). Check your firewall and make sure NC Launcher is allowed to download updates from servers. Problems like yours come up when the application is blocked, which eventually leads to its crash.
Use a cleaning tool like CCLeaner to clean-up registry entries. After you have performed these steps, install NC Launcher and download Aion again. It may take a while since the game's size is over 22GB. If you do everything correctly, you can be sure that the launcher won't crash next time you need an update.