When Patsy tries going to google.com, her network goes to "Facebook" with a message "unverified server" on all her devices. Leo says there's a chance her home network has been hacked. She should not log into Facebook. It makes sense that Google gets redirected so she can't figure out a solution to her problem. The chatroom says that it could be her DNS server. They advise going to http://22.214.171.124/, and if Google pops up, then there's a DNS issue. If it doesn't, then it may be the DNS has been changed on the router.
Steve is getting DNS errors and his internet connection is slowing to a crawl. Leo says it's likely a flakey cable modem. He advises taking the modem to the Comcast cable store and telling them it's broken. Ask them for a DOCSIS 3. It's fast and more reliable. Or, he can just buy a modem and avoid the monthly rental fee.
If that doesn't fix it, it could be malware. It is not unusual for malware to modify DNS. If he can't get to an antivirus page, that's often a sign of malware.
'Pinging' is a method of directly contacting a site just to confirm there's a connection there. According to the chatroom, if he has too many devices on his FiOS router, it could be preventing the router from connecting temporarily. Each device takes up an entry on the NAT table (Network Address Translation). Size limitations on that NAT table could cause the router to choke.
Leo says there's no reason why not, it's pretty complicated to setup, but sure. Search for "recursive query" for help on doing it.
Leo says that if Microsoft Security Essentials didn't find it, and Nod32 didn't see it either, chances are there isn't any malware on Matt's computer. He could have a browser hijacking object or a browser helping object.
Since it's doing it across more than one browser, it may be DNS Changer, which has changed Matt's DNS settings and is routing Matt's traffic elsewhere.
Leo's guessing that Carlos has a cookie that's directing the browser to the Chinese site. He should try clearing cookies to see if that resolves the issue. Or the ISP may be misreading Carlos WiFi as "China" rather than Chino. Go into Internet Options and reset everything. It could also be Malware, a RootKit, or a browser hijack that's redirecting his DNS.