I've just fixed a similar issue on my father's laptop. Babylon had taken over homepage and search provider for Firefox, Chrome and IE. Completely reinstalling Firefox had no effect as every time the machine restarted search/homepage preferences were returned to Babylon in all browsers. This seems to be a fairly common problem, but here's where mine got weird:

There was a program running (two instances) called Browser Manager. I found that all the time this program is running, your browser preferences will be overwritten either immediately, on browser close, or when the computer reboots depending on the browser. Note that AVG, Spybot S&D, and Adaware didn't find anything wrong.

Shutting down either instance results in another being run, making it impossible to completely unload the program (as you can only shut down one at a time). Of course, when the program is running it is impossible to delete the program files as they're in use. So...

Reboot in Safe Mode (hold F8 while booting and select from the menu). Locate and delete entire c:\ProgramData\BrowserManager folder which should now be possible (note that the ProgramData folder is usually hidden). Arguably, this will solve your basic problem.

Search registry using regedit and remove all references to both Babylon and BrowserManager (I searched for "babyon" and "browse" and verified each match to be sure - use F3 and delete any registry keys that are direct references to the problem files or related to browser search and refer to Babylon). The registry checking may beyond the more casual user, and if you're not comfortable don't try it - deleting the files should be good enough unless you're paranoid and want to remove every trace, like me.

To be super safe, search the computer's drives for "Babylon" and "browse" and remove anything related to Browser Manager (be careful as obviously "browse" returns a lot of hits and many will be legit). I found some files in AppData and a few hits for Babylon in the various browser's caches.

You'll obviously need to open your various browsers and reset homepage/search preferences. You can also remove the search provider completely if it's still there (choose another first as you can't delete your default provider). I also cleared all temporary files / history and did a quick eyeball of installed extensions/addons just to be sure. Doing this in safe mode has the advantage that your networking is disabled so there can't be any downloading.

Reboot and you should be OK.

I also checked msconfig for startup service or programs, but nothing seemed out of order, and obviously there wasn't anything in the Startup folder in the start menu.

Hope this helps someone!

BTW, I have no idea how this got installed in the first place. Any takers?

Finally I resolved my problem. Somewhere I saw a very technical removal of the browser manager but as stated above, it can be done quite simple. Thanks a bunch. I've read at least ten threads before stumbling upon this one. Happy now :)