Also, Is any antivirus or other security software installed? If so, which one? You should probably use it to run a full scan, and an “offline” scan if possible.
If you click into the address bar, then type :g then hit [space], you should see the following in the address bar:
Can you confirm that that is the case? Further, if you search from here, does it search via Google?
You may need to clear your cache/data for all time in the browser. Either that or something else is controlling what your default search is inside that profile (ie an extension).
Like Mattches says, I think something in that profile is controlling it.
If you can export/import your Bookmarks and passwords be done with it, you always have the option of creating a new profile and using that one going forward; and deleting the ‘problematic’ one.
@Oceanshu,
If you’re going to transfer that data to another profile anyway, it may be worth disabling your extension on your main profile first to check and ensure that one of them is not causing the issue.
Additionally, Bookmarks and passwords can be exported/imported easily, but there is no easy/straight forward way to move cookies from one profile to another without taking everything else with it.