i can search websites from bing but not google run websites like images, gmail.
So a CAPTCHA is issued when a site believes you are not human.
If you are coming from a shared connection/IP, and another machine on the connection/IP has been doing automated stuff w/ google services, anything further coming from the same connection/IP is challenged by google(it can’t tell the difference between two computers on the same connection).
If you are not on an shared connection/IP, are you running a browser plugin such as "TrackMeNot"? This could make you appear as an automated process too.
If the two above are not the case, then I would be worried about something you do not know about, like someone leeching off your Wi-Fi and doing ill(automated) things, or a virus running in the background off one of the machines on your network.
I hope one of these helps in resolution, let us know.
Good Luck.