strange that, only real suggestion i can make is to try turning off zone alarm for a moment (right click the icon and "shutdown zone alarm") note that your pc will be unprotected while doing this, as soon as you have tried it turn it back on Start/All Programs/zone labs/zone alarm security) to see if you can then connect to google. (dont forget to turn it on again) as you will be unprotected. ( i know i have repeated that, its important) if you still cant connect then at least you have ruled out zone alarm. also check your windows firewall isnt on and blocking the internet.
do an online scan at click here for virus/spyware etc
i have used zone alarm for years now along with AVG anti-virus and have had no problems (touch wood)
it might be the computer is going into sleep mode and not waking up properly (sort of coming back into safe mode instead of full windows),,,,,but then im just guessing.