Reinstalling OS X on a MacBook with dead hard drive and no recovery disc
Since you say it's a Core Duo and not a Core 2 Duo, I think that you've got one of the original white (or black) MacBooks.  If I'm correct, you're not going to be able to install Mavericks (10.9) on it.  The latest OS that your MacBook will support is Snow Leopard.  If I'm correct that this is your MacBook, you will be able to get a Snow Leopard DVD from somewhere (you can order it from Apple for $20) and install it via the DVD.  If I haven't guessed your Mac correctly, you can use this checker to figure out which one you do have.

If you are close to an Apple Store, it's quite possible that they will reinstall its original OS onto it for you.  Set up an appointment at the Genius Bar, explain your predicament, and ask for their assistance.