Let's slow down and take a breath here. I'm not convinced that the internal hard drive is dead, or even close to death. It's just failing to self-mount when booted in target drive mode.
passthehatchet, did you launch Disk Utility when you had the computer connected in target mode? My concern is that the drive may simply have catalog damage which is preventing the drive from mounting (and so preventing the installed OS from booting the computer).
The default fix for catalog repair is to reformat the drive. This create a new, clean catalog (a sort of invisible file index that allows the computer to track where on the drive each chunk of data is located). Usually, running Disk Utility won't fix it, but it's certainly worth a try if you can see the volume in the Disk Utility interface; fix both the physical hard drive and the virtual volume on it.
If Disk Utility doesn't work, the next steps require commercial software. Ideally, you'd like to recover the data on the drive, if that's possible. You can use commercial applications such as Prosoft's Data Rescue to salvage data of unmountable drives; copy it to a new external drive, then reformat the internal drive, install a new OS, and restore.
Alternately, applications such as Alsoft's Disk Warrior and Prosoft's Drive Genius can often repair a damaged catalog in place.
It's certainly possible that the internal drive is dead; after all, it's eight years old. but a platter drive rarely dies without warning; are there any other symptoms (noises, especially) that might indicate such a failure? Have you checked the hard drive data cable connecting the drive to the logic board, to confirm that it's intact and securely connected? If you're replacing the drive, you may want to replace the data cable as well.
As for operating systems, the Core Solo/Core Duo systems can run 10.4, but you can only install 10.4/Tiger from the original disks enclosed with the new computer. You can install 10.5/Leopard and 10.6/Snow Leopard from any retail disks; you can then update from the disk installations (10.4.6, 10.5.0/5.4/5.7, 10.6.0/6.3) to the final versions (10.4.11, 10.5.8, 10.6.8) using the Software Update system preference. 10.6.8 is the ceiling for Core Solo/Duo machines - basically, Intel machines from 2006.
In the event you can't get a commercial install disk any other way, there's a trick for getting a new copy of Mac OS X Server 10.6. 10.6 Server (a superset of 10.6 Client, which includes a variety of administrative tools for running Internet and local network services) is able to run as a virtualized environment: a mini-universe installed as an application on top of another operating system. Although Apple does not sell the four-year old OS in stores or online, it's available for US$20 if you call Apple's Sales number at 1-800-MY-APPLE (1-800-692-7753). They'll ship you the disks for 10.6.3, which you would then install (maybe using the installer to prevent installing a lot of extra admin tools) and update using Software Update.
10.6 Client disks are fairly common; Apple Stores were distributing them free for several months after 10.7/Lion shipped, because 10.6.8 is the floor for using the App Store, which is the distribution point for all Apple's newer software. You may be able to find those disks through eBay or Craigslist.