The fact that it's listed under the network connections with status of unplugged indicates that at a Windows level the driver is working fine.
Quote:
It worked well when i bought the ethernet cable joining from the Study room to Another Room which comp 3 is located
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That statement also implies that the problem is in the cabling. Also, in your pictures of the router there are three cables in the lan ports on the back but only two lan port leds lit on the front.