fstab is the file which helps linux decide which partition is to be mounted, which to be used as swap, which is the / (filesystem). Its essential to have that file.
As you said, you had the back up of fstab in your home directory, so as an initial step you can try to find the file:
Log in somehow (guest account or live cd or live usb with any linux distro). If guest is able to access /home/ directory.
Run the following commands in the Terminal:
cd /home/[user account you were using before]
find | grep -i back
If you are lucky, that should result in a small list of matching files. From that list check if you are able to identify the backedup fstab file. Once found copy the file to /etc using:
cp source-filename /etc/fstab
Alternatively, if you were unable to find the file, comment here back with the output of: