To access the internet from a home broadband network you need the router appropriately configured on the WAN or internet service provider (ISP) side and the attached computer to have an appropriate IP Address, Subnet Mask, Default Gateway and DNS addresses assigned to the network adapter.
Based solely on the title you should understand the following the belief here is that the PS3 is missing DNS address(es).
DNS address(es) are IP address(es) for servers that convert names like www.fixya.com
into IP addresses to send messages to normally.
Your ISP generally assigns DNS addresses for your use.
How do DNS addresses get into the computer's network adapter configuration where they are needed? There are two ways generally in home networks someone manually puts them into the computer or someone enters them into the router and via a service called DHCP they get placed in computer's network adapters configured to accept information from the DHCP service on the router.
If the heading of this problem is correct the PS3 appears to be complaining because the DNS address(es) have not been configured into the computer or the router by the user as expected by the PS3's network adapter. I have no PS3 experience however I believe this information may help to resolve your issue.
I hope this helps