The Avast Emergency Updater hang has been seen by others.
One reason identified is that Avast (possibly) contacts Google or other questionable sites during the run of that application, and if you have the MVPS.org
hosts file in place to block parasite web sites it won't be able to do so.
Temporarily renaming hosts - if you've installed it - to something else will allow the installation to complete.
Unfortunateliy I had a corrupted install after I had a hang much like what you're experiencing, and I ended up having to do a full removal, including a run of the Avastclear tool, followed by a reinstall of the latest release with hosts renamed in order to restore functionality.
See if changes to your settings in the Settings > Update section fail to stick. If that's the case, you'll need to go through a similar remove/install.
Avastclear :
http://files.avast.com/iavs9x/avastclear.exeSome folks recommend running a 3rd party (non-Avast hosted) tool, but I recommend against that.
I have reinstated hosts after the install. We'll see if the next release fails similarly - I hope not. Avast has no business failing because a web site cannot be contacted, ESPECIALLY not one of the ones in the MVPS hosts file.
-Noel