Try powercycling your router. You can ping hostnames but can you ping ip addresses? Sounds like a DNS recursive error.
Look inside your router also and try and ping the DNS servers it has stored. You can change them if they do not respond to known DNS servers in your country (if in AUS, try 203.2.75.2 or 202.92.65.252 or 202.92.65.254).
The fact that you can ping
www.google.com means someone is doing recursive lookups for you, but the real test is if you can ping public ip addresses. google.com is 66.102.7.147. If you cannot ping this number or any others for that matter, it is a problem with your DNS server (most likely your router).
Powercycle the router and keep a constant ping going to a public ip address and another going to
www.google.com (ping
www.google.com -t) (ping 66.102.7.147 -t). If you receive replys once your router is up and running then all is good.
Another thing to check is in interent explorer - tools - internet options - connections - LAN settings - make sure the auto detect settings is NOT checked.
If all else fails, assign yourself a static IP number on your NIC and in your DNS servers field assign a known public DNS server.
After that i'd be considering upgrading your firmware on your router or factory resetting it.
Let us know how you go :grinthumb