Sorry to hear it's giving you so many issues.
The newer beta versions had some problems, but the newest seems to be quite good.
You said that you uninstalled/re-installed avast, which got that back into working order. FF is your only issue now?
Since FF is just a browser, it's not too difficult to remove and re-install as well. I know you probably don't want to hear that, being an network administrator, but sometimes things take a bit of work to fix.
You could start with diagnosing your firefox profile
http://kb.mozillazine.org/Standard_diagnostic_(Firefox)
If that doesn't work, just nuke it and re-install. Backup your favorites if you need to, or use the sync function.
Personally, I like chrome, but that's just me.
Anyway, let us know what happens as you go along and I'm sure that we can get you going again.