I'd have far more faith in Avast's own software knowing what it's doing than in the Windows Action Centre.
After clicking on the Avast icon, go to Settings > Update and check to see that today's date is displayed against 'Current version' (i.e. 140913-0) and 'Release date' (i.e. 13/09/2014). If it is, your software is up-to-date (which probably explains why nothing happens when you try to update it).
If that's OK, go to the Task Manager. (In most versions of Windows you can get there by right-clicking on the Task Bar at the foot of your screen but I expect that Microsoft will have found a way to make it far harder in Windows 8!). Click on the 'Processes' tab (assuming that Microsoft haven't changed things too much!). If there's an option to 'Show processes from all users', ensure that it's selected.
If AvastSvc.exe is shown there, Avast's auto-updater is running and awaiting the next download from HQ. If avastui.exe is listed, Avast's anti-virus program is also running.