Unplug the router end of the patch cable first.
The RJ45 system relies on a spring tab holding the plug in which is released by compressing the plastic tab sticking out parallel to the cable. This may well be partially covered by a shroud.
Option two. Can you get at the RJ45 socket from the other (in)side? If it's a network card, remove it from the motherboard connecting strip & deal with it accordingly. If, as I suspect, it's actually of the motherboard or you have a laptop/small form factor then this can be a challenge. I've only had to do this once when my cat managed to chew through the CAT5 cable (I know ~ bad pun) too close for me to get a grip on the cable.
Do not be tempted to pull the end of the network cable — you may well be left with the RJ45 plug buried in the socket.
Sometimes that's just what it takes.
I've found that sometimes the release tab is caught on the inside of the port, and that by gently pushing INTO to port while first pressing the little plastic release tab to uncatch the tab and then pulling out, you'll have some success. But sometimes it just happens that you need to pull, and pull, and PULL, just like you did. – music2myear – 2011-09-26T21:57:39.137
2I'd replace that cable as quickly as possible. – Sarge – 2011-09-26T22:46:10.983