I was wondering if Google could be made the default search engine by pressing the 'Search' button rather than Bing. I'm not sure if Microsoft is okay with this.
Considering Bing is not just used for mere searching, but also integrates with the marketplace, and have support for places, vision, music and voice-search, replacing it with Google would require a large number of Google Services, and not just the search-engine.
From a Microsoft Answers post:
The default search engine is indeed set by the provider. At the moment, there is no way for the end-user to override this default. Many have asked for this feature, and I really hope we get it in a future update as the current behavior is anything but user-friendly.
So there doesn't seem to be an official way at the moment.
There is a homebrew tool that could allow this, but you'd need a developer-unlocked phone, and it only seems to change the behavior of the button within IE, not system-wide.
It is possible to open Google from the the search button by changing your search language:
SETTINGS system language+region Browser & search language Bashkir (Russia)
Not all languages will work for this. I recommend Bashkir because it will make your phone open Google, but not make Google attempt to translate the results you find.
If the above doesn't work, you may have to change another setting:
SETTINGS applications Internet Explorer advanced settings Default search provider
Change default search provider from Bing to Google.