PS4 not working with LAN Cable. What's going on?

First, Get over to the PS4 Menu XrossMediaBar (XMB).
After you are at the XMB, you need to scroll right to the Settings, then to Network and then you need to click on “Set Up Internet Connection”.
There you will have to select either WiFi or wired LAN cable. Since you had the problem while connecting to your WiFi, you’d want to choose WiFi in this option.
After you select WiFi, you need to select ‘Custom’ and then you have to select the WiFi network.
You will see a field where you will have to enter the password of your WiFi network. If you are already using that WiFi on your PS4, the password would be automatically saved and you won’t have to enter it again.
After entering the password, you need to select ‘Automatic’ in the IP Address Settings.
You shouldn’t use the DHCP Host Name and you have to select ‘Manual’ in the DNS Settings that you see there.
In the DNS settings, you can enter the following servers in Primary DNS and Secondary DNS fields:
Primary DNS: 8.8.8.8 and Secondary DNS: 8.8.4.4
After you set the DNS, you should click ‘Next’ and select ‘Automatic’ in the MTU Settings. You shouldn’t use any Proxy Servers there.
After you follow all these instructions, you are finally done. Now, you have one thing left to do.
You need to Test Internet Connection.
If it still didn’t work, you can try the following servers in the DNS Settings:
Primary DNS: 208.67.222.222 and Secondary DNS: 208.67.220.220