My iMac has all the latest software running.
Aperture 3.4.4 and MacOS X 10.8.3?
Did you install any new software (Applications, fonts, drivers, plug-ins, firewalls, ...) lately or update something? Did you run cleaner applications? Is Aperture the only application giving trouble?
Tried opening another, smaller, older library...same thing.
Can you at least create a new Aperture Library and open it? (Launch Aperture with the options key ⌥ held down and select other/new).
If that does not work, can you launch Aperture from a different user account - see http://support.apple.com/kb/TS4053?viewlocale=en_US&locale=en_US ?
If Aperture works from a different account, there may be something wrong with your settings in your user library. Try if remove the preferences or the presets helps as described in http://support.apple.com/kb/HT3805
If it does not even work from a different account, then reinstall Aperture.