Very strange nobody has looked past the surface and seen the real question:
How to recover data from the filesystem of a Raspbian SD card?
Answer: Your laptop (Windows)
cannot access the type of filesystem Raspberry Pi uses. Windows can access NTFS partitions and FAT32 partitions. That's why your laptop likely showed you only the boot partition, but not the root partition.
The root partition is EXT4, a type of partition that Windows is clueless on how to show you.
If you have a linux laptop handy, use that to access the filesystem. (Raspbian is Linux)
But if not, probably the easiest way is to
buy a second SD card which I'll call card 2. Boot the Pi on card 2, plug in card 1 using a usb card reader, and copy off the files.
To keep this from happening again,
back up your Pi regularly. Easy - just use SD Card Copier from the menu to copy everything from card 1 to card 2.
If card 1 fails, gets lost, gets cracked, or doesn't boot, just switch to card 2 (the backup) and keep going.
Sidenote: If accessing card 1's filesystem is not enough, but you need to
boot it like you asked - easy. I've made a handy Raspbian utility called Pi-Power-Tools to edit Sd cards and Raspbian images.
In your case, you would be interested in the boot option: select the usb card reader containing the damaged card 1, then click boot.
You can play around with the desktop and type commands in the console, just as if you actually booted card 1.
https://github.com/Botspot/Pi-Power-Tools