How to unplug a network cable that's stuck?
Glad it's sorted. For the future this often works and doesn't need a lot of brute force:
If the plastic clip has 'stuck' or lost its springiness so it cannot be squeezed:
Gently slide off any cover over the connector
PUSH the connector IN a little bit
Slide a piece of plastic between the clip of the plug and the body of the socket while pulling gently on the plug to remove it. I use the end of a small tie-wrap (plastic cable tie) as they are very thin, but a 'pointy' pen top can work too. You can use a small jewellers' screwdriver but I prefer something soft. You should try and press the plastic/screwdriver in as far as possible (but gently) as you simultaneously pull on the connector..
I DID IT!
I was finally able to remove the cable by twisting it vertically while applying a great deal of force. This made me a little nervous due to the amount of pressure I was applying - but it worked.
I'll probably be a bit more careful putting the cable in next time.
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.