OMG, I solved!!!
Do you want to know how? Well, just for fun I was exploring Settings. I noticed the tab about proxy in the Updates tab, and the problem was there!!
I had
"automatic detection (use Internet Explorer settings)" (I'm using italian avast so I don't know what's the true english name, but i'm talking about second option), I changed it with
"direct connection (no proxy)" (the first option) and he started updating!!!
So, to finish this story, F**K IE, long life to Firefox & Chrome!
Regarding the updating problem, sorry for the blatant question, but you aren't using a pirated license file for avast 5, are you?
As I wrote in first post, i'm using the free Home, obviously with a genuine licence