Tools > Manage Add-Ons > Search Providers
uninstall it from add remove programs if it is listed there.these things are really annoying :/.
also take a look at step 2 and 3 here http://www.sevenforums.com/software/198401-cant-remove-ask-com-search-program-2.html

since when are you having this babylon issue? cause i tried helping one person with the same topic and nothing worked, he had to do a clean install.
How did you get Babylon? You could be infected. Some times you have to get rid of things like this in safe mode. I use Search Everything in safe mode to remove stubborn things. You must be very careful with Search Everything. If you remove the wrong thing it's gone. Other programs you can use are Ccleaner and Revo. Once again you must be careful. If it were my computer after getting rid of the Babylon I would run scans with MSE and Super Anti Spyware to make sure things are clean. I had to remove the Ask Tool bar with Search Everything in safe mode.
since when are you having this babylon issue? cause i tried helping one person with the same topic and nothing worked, he had to do a clean install.
It's always been an issue. You mean a clean install of IE9?