You could try um...
Use Add/Remove Programs in the control panel to make sure it's removed.. then follow these steps:
1. Open the start menu and type in "Regedit" in the search bar, open it up (you may get asked if you want to do this, press yes)
2. On the left panel Make sure the top of the list (Called "Computer") is selected (so that you are on the top of the list)
3. Press F3 and search for "Babylon"
4. When it finds something, simply press delete and delete it. *Note it may take some time for it to search
5. Repeat steps 3 and 4 until it tells you something like that it couldn't find it or that it finished the search, but it doesn't show any results.
Once that's done, open up chrome settings, change google back to default (and remove the babylon ****). Also uninstall any hidden plugins or extensions that might have been re-added. You can also go to type "about:plugins" and open that page to view all installed plugins (and remove/disable them).
To test.. simply reboot your computer and see if it fixes the issue, if not change back again the settings and plugins in chrome (no need to re-do the regedit part) and restart again to test if it works now. If it still doesn't work, I'm not sure why...