Instead of all the somewhat radical solutions posted here (e.g. formatting and starting from zero) I suggest taking a look at the internet settings (specially the proxy ones) of Windows (which are the ones used by IE, but might not be used by Chrome) and comparing with the ones set on Chrome and see if they are different.
Do this even if you don't use a proxy! Keep on reading and you'll understand why.
To see internet settings on Windows, the easiest way (no need to open IE) is to go to Control Panel (make sure you choose to show all icons, and not the categorized view) then look for the Internet Settings icon. Now I'm not sure what to do now (I don't use Windows for quite a long ago) but you should search for the proxy settings.
To see the Proxy settings on Chrome, click the wrench icon on the toolbar, then click on Options, go to the "Under the hood" tab, then click on "Change proxy settings".
If both settings are the same (e.g. do not use proxy at all), then you should try the solutions mentioned by the other posters (specially scanning with your AV after updating it). If you see some strange settings you didn't setup on the settings, select "Do not use proxy" or "Connect directly to the internet" (can't remember what it says exactly) (unless you indeed use a proxy), and try connecting using Chrome and IE again.
What I'm thinking on is that some program, most likely a virus, changed the proxy settings on your computer (on Chrome, on IE, or on both) to some dangerous proxy which is going to infect even more your computer (for example, with methods that involve redirection of addresses - you type google.com on the address bar but in fact the proxy is taking you to a dubious copy of Google). This happened some years ago on the computers of my school's library, and the solution was wiping the virus using a powerful Antivirus (in that case, the only solution was running the AV from a pendrive, but now that doesn't matter) AND setting the proxy settings to the default ones, because the virus had changed them. If this failed, the only thing to do was formatting and installing the OS again, loosing everything (that didn't matter much in that case because they were public computers, but I guess it matters on your comp, so make some backups first 🙂).
I hope this helps.
PS: If someone can correct this post, please do it... I don't use Windows on my main comp since September, now I use Ubuntu, so some details about the procedures might not be correct. However, the main idea is here for anyone who might find it helpful. 🙂
