I need to restore my data from a non time machine manual backup
You can get your data back.  It might be fairly easy with migration assistant.

There is probably some way of coping the data back &amp; getting your mac to boot.

What OS X are you running? 

What you did was drag the Macintosh harddrive Icon on the desktop to the external folder?

You may want to post your question here:
https://discussions.apple.com/community/mac_os/mac_os_x_technologies

Or the discussion for your OS X version.



Whatever the case, you will be able to recover your data.  You may have to copy over it folder by folder.

I believe that you can use migration assistant to move everything back.
Macintosh-HD -> Applications -> Utilities -> Migration Assistant

In that case, re-install the OS. Then run Migration Assistant



What is the state of your machine?  Is it working?  How did it crash?