Use your live usb to boot.
mkdir ~/mnt
sudo mount /dev/sda1 ~/mnt
The folder ~/mnt/home/* should be of use just retrieve the files you need to the cloud or another usb stick. Looking at your fdisk output is probably not sda1, but 2 or 3 is what you require. If you were setup with a seperate home partition then the folder ~/mnt/* is where to start looking