After months of wasting my time trying to persuade my type cover to work I gave up. I bought this instead, and although it is early days, I am happy to have my Surface Pro 3 back again.
https://www.amazon.co.uk/gp/product/B01AJOX7LU/ref=ppx_yo_dt_b_asin_title_o00_s00?ie=UTF8&psc=1
Thanks for this suggestion, I'll consider that option as well.
(But before anything else, after the problems I caused myself this evening, I'm going to get on with my regular weekly data backup!)