Check Internet Connection
The first thing you should check is that you have an Internet connection. Using another computer on your network, make sure that you're able to connect to other websites. Reset your modem and your router to kick-start your connection. If the Internet is still down, it may be that your ISP is having issues. Contact your provider to find out if there's an outage in your area.
Check PS3 Network Settings
If your network is working but the PS3 still cannot connect to the Internet, your next step should be to check the network settings on your console. Go to Settings and select Network Settings. Make sure that the Internet connection is enabled. You can reset the connection by selecting "Internet Connection Settings" and choosing the easy installation. After a moment your PS3 will detect the Ethernet connection automatically and test the connection.
Check Router Settings
Open your router settings using another computer connected to the network. Check your router manufacturer's website for details on how to open your router. Once inside, check that your router is "Keep Alive" -- which stops the router from shutting down your connection using "Connect on Demand." Check that your router isn't using MAC address filtering, which limits which devices can connect to your network by this. If it does, add your PS3's MAC address to your filter. The MAC address is available in the Network Settings menu, under Settings and Connection Status List.
Check Hardware
When all your other settings are in order, check that your hardware is all in working order. Check that the Ethernet cable is in working corner, with no missing pieces or damage to the cord. If possible, use a shorter Ethernet cord; cords longer than 25 feet will have a weaker connection than shorter connections. Try using a different Ethernet cable. If you're using a router, try connecting directly between the modem and the PS3 to see if removing the router resolves the problem.
Resetting PS3 Defaults
The last resort to connect your PS3 to the network is to reset your PS3 to the default settings. This does not remove any of your files, but does change all the settings on your console. You can do this by going to Settings, System Settings and then select "Restore Default Settings." Follow the on-screen prompts to reset your settings.