NetworkManager broken after upgrade to Kubuntu Saucy

After seeing your other problems, I'm pretty sure the problem is with policykit or consolekit.

make sure you have policykit-1, policykit-desktop-privileges, polkit-kde-1 and consolekit installed.

if they are installed try reconfiguring them (sudo dpkg-reconfigure policykit-1 policykit-desktop-privileges consolekit polkit-kde-1).

If the root user can do something that you can't, it hints towards an issue with the policykit privileges.

Open Terminal (Ctrl+Alt+T) and run

sudo service network-manager status //Note the process-id (995 in your case as per the comment)
sudo service network-manager stop
sudo service network-manager status //See if it's still running; if not, enter next command
sudo dpkg-reconfigure policykit-1 policykit-desktop-privileges consolekit polkit-kde-1

to reconfigure them.

Then run

sudo service network-manager restart

and see if it's working now.

As for the WLAN/WiFi not working even as root (if the issue is still unresolved), please update the Q with the WLAN NIC name. The drivers may be faulty and you may require alternate ones.