I didn't reply, sorry about that, but decided to do this update post instead, to let you all know I HAVE CLOSED THE LINKED -IN ACCOUNT, yay me!
Perhaps last night, when I tried over and over, someone at the other end was napping on the job.
I turned on the laptop five minutes ago and straight away went to the Linked In site and managed to close my account.
Any of you who have an account there and wish to close it, follow Lee's excellent instructions, which is what I was doing most of last night, but today it worked. Finally.