Hi.
I am assuming that you are using a desktop PC, therefore with a pair of speakers or headphones plugged into the rear audio jack.
As I'm sure you know, the Ethernet port has no direct influence on the sound however, it could affect it due to one of two circumstances. First, check the sound jack and ethernet plug that they are both plugged in correctly as they can sometimes short out across the IO shield (metal plate at the back of the PC).
If this is not the problem, next check to see if the two cables are near each other. If they are, think about separating the cables by tying them back or investing in some graphite-collars to reduce the interference. A lot of people don't believe the collars do anything but they do help.
If this doesn't work, I'm afraid I don't know what else the problem could be, sorry.