Hi
Sorry after i posted about system rescue I re visited using it, and it doesn't have as easy access to DDrescue as I thought so I would give that disk a miss.
Suggest you cover all possibilities with Hirens Boot disk from here
https://www.hirensbootcd.org/And yes, use your desktop to download and make either a pen drive or CD. Boot and run Recuva to scan the Laptop drive for your files