This is boring, but I have to finish the story. 1st, I discovered the right digital converter for Grandma, and though sold at John Lewis, was in their warehouse rather than their shop. The next day I was in Sainsburys for tea and my father said maybe they've got digital TV boxes. Not only did they have them, they were the same as the ones from John Lewis and £5 cheaper. It's now up and running perfectly.
I also re invested my £20 in a normal black and silver keyboard with chunky keys, an arm rest and hot keys that had a very rough CD installation (crash!). Now half of them work, but I can live without them if I have to.
Otherwise my car is in the garage for 24 hours so anything I need to do in the house may actually get done at last.