In reply to jethro kiernan:
I think you are correct not to use the computer, it is not yours if you are going to send it back. I'm sure it's a gray area legally, but if you start to use that computer for anything more than seeing if it was as described, then you should keep it for the price you paid.
All this lady owes you is to pay for the postage back and refund any money you gave her as long as the computer is in the same shape it was when she sent it out. She also owes you an apology for her mistake costing you time, but that's the risk you run shopping on Ebay. That's why it is cheaper. If you want quick resolutions to any possible issues, shop at Jhon Lewis.
She should act as quickly as possible to take the computer back and refund your money, as soon as you request a return. Have you actually done that? It seems like you might still be asking for a partiaal refund she has already said no to.
Personally, I feel that your need to have a laptop right now is not her responsibility. If you lost a thousand quid worth of work would you try to sue her for that? Of course not, she has no control over your work requirements and can't be held responsible.
I'm not having a go at you, just trying to help you see the other side of the arguments. Good luck sorting it out.