Hi! From what you stated I'm guessing the optical drive is powered on and accepting media. If you go into About This Mac, does it show that an optical drive is connected? If so, and it's not reading media and/or kicking out all media, it may be a bad drive.
While you're booting from an external hard drive, I'd also go into About This Mac and see if it shows your local hard drive at all. If it does, you may want to go into Disk Utility, format it (if it will format), and then see if you can re-install the OS via target mode with the OS media in the other machine's optical drive.
Hopefully this will help. If not, let me know as many details as possible and I'll try to assist further. Thanks!