Random sites and all sites with antiviruses do not open. How to fix?

Question

Browsers

Different sites do not open, including sites with antiviruses. The Internet is working.
Sites are pinged. Sites do not open by IP address either. I scanned the computer for viruses with different scanners, about 50 different viruses and Adware were found, but the sites never come off.
windows 7 sp 1
HOST clean. The HKEY_LOCAL_MACHINE\\SYSTEM\\CurrentControlSet\\Services\\Tcpip\\Parameters\\PersistentRoutes registry is clean.
I noticed that large sites such as google and Ebay first try to load for a very long time, and then they still load.
Where to dig further? I don't want to destroy the system...

Answer 1

1) Boot from livecd, check the Internet and make a trace.
2) If livecd does not have drivers for your network card - hook up a usb-modem / phone in modem mode to the running system, check the Internet and make a trace.

Answer 2

tracing