I had no problem with google.com winXP SP3, avast free using firefox and I did the beta testing after 2218 pre 2225. So this isn't across the board with XP firefox and avast.
The only issue I had was with yahoo.com images not loading, which is different, thought the disablement of HTTPS appears to resolve the google.com problem.
Unfortunately the OP hasn't given us much to work with:
I can't access Google.com using Firefox and it won't allow me to connect to Mozilla
Screenshots of the 'why hdortch can't access google.com,' e.g. error screen or alert window, etc. would help.