Simple anwser, yes.
Ethernet.
An ethernet cable is a network cable that is used to connect your computer or other web-enabled device to the internet. You can use an ethernet cable to establish a wired connection from your computer to a router or modem to connect to the internet.
For your PS3 connection you need WiFi or an ethernet cable that is connected to the internet. The HDMI cable only connects the PS3 to the HDTV and will not provide the internet connection.
you plug in a ethernet cable to your router and then to your computer
Xbox Live requires an internet connection, either by wireless adapter or ethernet cable.
If you don't have a wireless connection, then yes.
To connect your device to the internet using an Ethernet cable adapter for the wall, simply plug one end of the Ethernet cable into the adapter and the other end into your device's Ethernet port. This will establish a wired connection to the internet through the wall adapter.
No it needs an ethernet cable connection to an internet service
You did not put your Ethernet cable in the LAN port on the router.
No. The PS3 can only have a wired connection with an ethernet cable. The only other connection that is possible is WiFi. The PS3 can only connect to the internet with WiFi or ethernet cable no other type connection is possible. You can not use the HDMI or USB port to connect the PS3 to the internet. I do not believe a router can be connected to the internet cable without a modem or that you can have cable internet without a modem
A PS3 has WiFi and you can put the router next to your modem. The only thing the back of a PS3 uses for the internet is for a wired connection with an ethernet cable to your router or modem instead of a WiFi connection
With an ethernet cable. (male)