Are you able to invoke softwareupdate from command line?
softwareupdate -l
man softwareupdate
If you wanted to see what your options are for software update just open a terminal windows and type softwareupdate... You'll get a list of options.
If you just want to automatically install all available updates the following command will work. It does require you to enter the password of an authorized user.
sudo softwareupdate -i --all
Let me know if that helps.
Also, have you checked disk utility and repaired permissions on your 'Macintosh HD'? That should probably be a first step.