I doubt a hardware problem with my ethernet device. I'm unable to connect to Internet. How can I verify if it's a hardware issue or not?
If you have access to a second computer, connect it to the same ethernet cable and port. If that computer gets internet access (be sure to disable wireless, so you know it's connecting via ethernet), the first computer's ethernet device is faulty. If the second computer does not get internet access, try swapping the ethernet cable for another (the first could be badly crimped or faulty in other ways), and try another ethernet port.
Full hardware testing is difficult. There is an application Tech Tools that can do pretty decent hardware checks on OS X.
Honestly, I you can see information about the NIC under Apple Menu, About This Mac, More Info, Ethernet Cards I would say the device is good. This isn't a 100% guarantee but with the frequency or hardware failure vs network issues I would say validating this would make me look into the network issues first.
I think simply connecting the network cable to the ethernet port and turn on the computer. Now it's not turning no the LEDs which means the hardware seems gone!