I think there is are legitimate questions to ask about this.
On the face of it is clearly AVAST which is flagging what looks like the normal Google start page, which milllions of people use as their home page, as being an "unsafe search engine". But all may not be as it seems.
I've just been to the Google start page yet there's no problem for me with Firefox, Opera or IE and the AVAST WebRep icon is showing all OK.
So why is the OP getting that AVAST message?
As the others here have said the important part of the AVAST warning is the "Show Details" button.
That will tell you where it thinks there is a problem.
The fact the warning appears when IE launches with Google as the home page does necessarily mean that Google is the culprit. It is a warning about a particular search engine which is installed on IE. Perhaps it is a dodgy secondary search engine that has been added to IE by the user or, much more likely, by some sneaky malware.
If it is the later then AVAST's or IE's own built in protection may have been stopped it hijacking your home page too.