Etherne is for a network connection and graphics media is for your monitor display. Ther drivers are totally different.
Go into Control Panel then System and kn XP click Hardware then Device Manager - the Hardware tab doesn't exist in Vista or Windows 7. Look at Network Adapters and if there is no Yellow mark beside it, it probably works and if you can get online, it almost certainly works.
Next, click on Display adapters and see if that has a yellow mark. If either do, click on Driver then Update Driver and see if that improves things.