I haven't seen any recent complaints specific to Blizzard games. What error, in particular, are you getting? Could you share a screenshot with us? If I knew the error, I'd be in a better position to help you.
Which websites are you unable to visit? Do you get a browser error when this happens?
If you could also further elaborate on the local ISP issue you mentioned, I can determine if I need to escalate your concern to a tech.