If the problem is only in Opera, you can check the settings Brandauer staff. You can diagnose problems with your network adapter (to Clean ARP, DNS, NetBIOS caches. Really don't know if that made CCleaner).
As organized access to the network via a router, ADSL modem, dedicated line? How is the network connectivity — VPN, PPPoE? If the router is to check the settings and reconfigure again, check the blocked traffic. I would have played around with netstat (in particular, at the time of connection to the site), looked at network activity of applications.
From the category of mysticism — may be joined Opera proxy servers? You should also try Internet options — there may be something written left.
It would be nice to check hosts.