The Screwdriver Technique -
More than likely, wiggling out the Ethernet cable will not work. But never fear, there is another solution. Simply find a small flathead screwdriver and very carefully insert it underneath the Ethernet's plastic tip. This is the part of the cable that has more than likely broken off, and thus, the reason why you can't remove your Ethernet cable. By applying a small amount of pressure from underneath the cable and pulling at the same time, you will probably succeed at removing the Ethernet cable. It may take you a couple of tries, though.
http://www.helium.com/items/1363770-how-do-you-remove-a-jammed-ethernet-cable
I would add: try with a needlenose or skinny long nose pliers, top to bottom, keeping pressure on the release tab as you wiggle it out. Might put some thin non-skid rubber such as you might find in a bicycle tube over the connector to help improve the grip.