Help! Sites "can't verify identity"

I've had this problem for a long time and it's now affecting my Gmail. When I try to log on to sites like Facebook, imdb and now Gmail, I get a box that says "Can't verify the identify of www.gmail.com." I've cleared cache, cookies, history and restarted, but it happens in all my browsers (Safari, Chrome and Opera). After I click through the error box, I go to a blank page with only the words:

Invalid URL

The requested URL "/", is invalid.
Reference #9.37c78f18.1327969609.29c20336

What can I do here? It only happens on my MacBook (not iMac on same connection) and at completely random times. It eventually goes back to normal after a few hours.

My Son is Having a Similar Problem--Locked out of iCloud

My son is having a similar problem today. iCloud says it doesn't recognize his identity. It asks him to reset his password, and because he can't get his email, he has to use the security question option. When he does that, he's asked for his birth day, but when he plugs that in, the response again is that the answer is not correct. He's now been locked out of his account for 8 hours, Apple Support is closed and he NEEDS to get his emails. Can anyone suggest a solution?