Richard, thank you for your help but I think we had better leave it there.
As I said, I am not a technical person and I wouldn't recognise the Network Interface Card if I tripped over it let alone the cable it is connected to.
My main thought when I asked the original question was there might be a virus or worm that was causing it to boot up on its own, I did not think it could be a hardware problem after 18 months of trouble free service.