Well there is the easy solution and the easier solution, but both involve you spending money on a new hard drive if you want to fix this computer.
- Go back into the BIOS and change the SATA Mode under drive options to ATA from AHCI and save settings.
- Boot the drive in Safe Mode by pressing F8 repeatedly until you get a list of boot options.
- Pop in a flash drive when windows gets into safe mode and start transferring your files.
- Go to newegg.com, or a simliar retailer, and pick up an external enclosure.
- Install the hard drive in the enclosure and connect it to another computer to retrieve the files.
Please note that these solutions will only work if the drive can still spin up and maintain normal operations. If your drive clicks or does not turn on, there is only one hope for your drive and unfortunately most professionals charge near to $1000 to recover from disk.