Thank you so much to the people who commented on my original post telling me to try that approach as the laptop wasn't that old. Particularly to Jackie (who noticed that it wasn't that old, because her laptop is the same age), and Ami, who mentioned the particular law I should reference. I really didn't think I was going to get anywhere with it, as I believed that HP would just shrug it off - so glad to have them offer to repair it, without any complaints or queries!
That's £400 I'm not going to have to spend when we don't have it!
