Well, if a chat program is working, then you definitely have a valid IP address, so it's either a name resolution issue, a firewall issue, a proxy, or (assuming you're running Windows) a malware issue. 4 possibilities is easier to go over than 65,536.

Name resolution
If you can ping 206.190.60.37, but not yahoo.com, then you have a name resolution problem.
If you're running Windows, try typing "netsh winsock reset" into a command prompt window (with administrator privileges) and restart the computer. If you're using your ISP's DNS, try switching to Google Public DNS, or vice versa. Name resolution can also be a router issue, but I'm assuming that the computer you're using to post goes through the same router, and would therefore be affected if that were the case. If that assumption is mistaken, try removing the router.

Firewall
A lot of people only think they've disabled their firewall. Typically only Mac users are correct, so once again, I'm going to assume you're on a Windows-based PC; Ensure that you disable both any software firewall you may have installed (would be located in the system tray in the bottom right) and Windows Firewall from the control panel. Most people forget one or the other. A lot of malware programs act like firewalls. The last thing to try for a firewall problem would be the msconfig utility. Go start->run (or use the search bar)->type "msconfig" and go to the services tab. Check "Hide all Microsoft services" and then "disable all"; then go to the...er...last tab (it's been a while, and I don't have a 'doze machine to check what it's called) and disable all on there as well. Hit OK, restart your computer, and if it works, start adding things back in in msconfig until you figure out what it is that's buggering you up

Proxy
A lot of people, especially Windows-using Facebook-goers, are getting malware proxies installed by a Facebook-driven password-stealing trojan. From IE, go to Tools -> Internet Options -> Connections and pres "LAN settings." If anything's checked there, uncheck it and hit OK. You should now be back on the internet. Now run a virus scan. The moral of the story is: Facebook is the internet equivalent of the closest brothel to a Navy base. If you go there, you're going to get infected. So use protection.

Malware
Malware can do freaking everything. Your best bet is to use your working computer to download everything from mytech.me - Technical Assistance Site by Marcus (preferably from the original sources, since they may have been updated more recently. It's also generally a good idea not to trust third-party sites, but I know the stuff on kgb123 is clean because I freaking put it there), stick it on a usb stick, and run them on the broken one. If you still have malware on there after running at least MBAM and SuperAntiSpyware, then you're probably stuck doing a full format or paying some PC tech a ludicrous amount of money to format it for you. So the moral of the story in that case is: Get a Mac. It's only more expensive if you don't factor in the extortionate rates PC techs charge to remove Facebook viruses.