I remember problems with safezone browser when I installed avast. Don't really know what I did to solve them, alas.
Can you start safezone browser by itself? It starts like any ordinary version of Chrome, not even inside the sandbox. C:\Program Files\AVAST Software\Avast\sfzone\SafeZoneBrowser.exe. Or wherever your avast program directory is.
Still problems browsing?
Can you start safezone browser in the sandbox?
Still problems browsing?
Is the safezonebrowser when started from the avast UI still unresponsive?