Sounds like the boot sector of the internal drive is corrupted.Try using another computer to download ubuntu to a usb stick.Google this to follow the instructions.What you need is Gparted which is a version of Partition Magic.
Then Go to the machine you have trouble starting and try to alter the boot sequence to USB from startup.No need to install linux, just run it from USB and let Gparted …you may need to disconnect the internal drive and load the usb linux first.Then reconnect drive and rescan drives using Gparted.It shoukd allow you to read the files and correct boot record.
It is possible to copy the contents to another drive and or correct the boot sector.I wouls save any files BEFORE changing or correcting the drive.There are other tests you can run to see if the drive is failing of full of bad sectors.
I have also done this on a windows machine.Also you cam use Hirens boot disc.Again google, download Hirens to USB and connect the internal drive via correct leads to the windows machine.Start USB first, load Linux Gparted..
This is enough to run a chkdsk and correct boot sectors and MFT….as well as copy clone files.
Need further help , i will try to help.