You've made no mention of Babylon or the Babylon Toolbar, but Search the web seems to have a connection. This link may prove useful:
http://www.anvisoft.com/wiki/how-to-uninstall-babylon-toolbar-completely-permanently.html
If that gets you nowhere...
Try this:
Firstly, boot your computer to the Safe Mode menu screen. You do this by repeatedly pressing F8 as soon as you boot up. Once there, use the arrow keys to highlight Safe Mode with Networking. Continue to boot from there, by pressing Enter. You will now see some drivers being loaded. There will be a pause at some point. This usually lasts for no more than 30 seconds.
Start Internet Explorer, and when the program is open, click on the Tools menu and select Internet Options.
Now click on the Connections tab.
Now click on the Lan settings button.
Where it says Use a proxy server for your Lan, ensure there is no tick in the box, then press the OK button to close this screen. Now press the OK button to close the Internet Options screen.
If that's all okay, remain in Safe Mode and try this...
Most redirection problems (including Google) are caused by the Alureon rootkit. TDSSKiller will remove it. The MBAM link is included so you can scan for infections you may not be aware of.
Download and run TDSSKiller.exe from Kaspersky Lab. It's tiny, and takes just a minute to run. It hunts down and kills a specific family of rootkits:
http://support.kaspersky.com/faq/?qid=208280684
Regardless of the results, download the free version of Malwarebytes' Anti-Malware (MBAM). Install it, get updates and run a full scan (still in Safe Mode). This is a direct download link. Copy and paste it into your browser’s address bar, and press Enter.
http://www.myantispyware.com/mbam
After this, try rebooting normally. If that's successful, I recommend you run another full scan with MBAM. It will detect malware that wasn't running in Safe Mode.
You should now delete TDSSKiller.exe, as updated versions are often made available. Malwarebytes' Anti-Malware can be easily uninstalled, should you wish to do so, but it may prove to be beneficial in the future.
Hope this helps.