Hi
+I was unable to find an external DVD player locally that works with 10.2.8, so I found one online that said it did--a Sony DRX-830UL-T. Turns out, this DVD player/burner will only burn in 10.2.8., not play.+
That sounds slightly odd to me as it's normally the other way around! Most DVD drives are supported for basic reading/playing, because if you're attempting to boot from a DVD in the drive, the OS isn't even loaded until the DVD has been read. Normally the problem lies with burn support. Also, if you're burning a disc, it's normally read/played back to verify the burn was successful.
An internal DVD drive such as a Pioneer DVR-112D may have been a better choice. They're generally more compatible and cheaper (~$40) because you're not paying for an external FireWire/USB case, cabling, bundled software you don't need and fancy packaging etc. Installation is also fairly easy as well. Instructions including a QuickTime movie can be found here:
http://docs.info.apple.com/article.html?artnum=75312
When you say the Sony drive won't play, what happens when you insert the OS 10.4 DVD? Is it spat back out? Can you hear it spinning up? Does the DVD appear on the desktop?
Edit - I seem to remember Macs don't officially support booting from a USB device. Is the external DVD drive connected via USB?