rossnixon,
Whilst I personally have not used FastCache, from what I have read it is a simple caching DNS proxy server that sits between the browser and the DNS servers on internet that map domain names to IP addresses.
Avast's Web shield scanner also sits beween the internet (Port 80) and the browser so perhaps the avast shield, as the last installed has effectively cut off the internet connection to FastCache (I am assuming that FastCache would also use port 80.
I haven't been able to find any specifications published for FastCache to indicate whether it has configurable ports that would allow it to be tacked on in series between the output of the Web Shield Scanner and the input of the browser.
You could terminate the Webshield and disable its Service, but that would disable a part Avast's protection that I personally think is worthwhile. Others may argue that the Standard Shield should still protect you - I guess it's your choice.