Is your existing installation still working to some extent? If so, with a spare HDD you could use your existing system to install a clean El Capitan to that https://support.apple.com/en-gb/HT202796
then, in your exiting system set the external drive as the startup disk (in system preferences) & reboot.
If all is well you'll be running on OSX on the external drive.
Use the same procedure to install to the internal drive which the OS on the external drive will 'see' as spare.