I can't install iTunes 10 on mac os x; therefore, I can't sync new iPod devices with my old iTunes version 9?

That's because in order to install iTunes 10 you need to be running a minimum of OS10.5 - Leopard and you have OS10.4 Tiger.

10.5.8 is the latest version of OSX that will run on a PowerBook presuming your model meets the minimum system requirements http://support.apple.com/kb/HT3759

and you can track down a retail copy somewhere - Apple no longer sells Leopard.

Mac OS X 10.5 Leopard installation system requirements

http://support.apple.com/kb/TA24950

Leopard is no longer available at the Apple Store but may be available by calling Apple Phone Sales @ 1-800-MY-APPLE (1-800-692-7753).

If you can't obtain a retail install DVD from Apple, look on eBay or Google the installer part numbers to possibly find at an on-line store. Here's what to look for:

MB427Z/A Leopard 10.5.1 install DVD

MB576Z/A Leopard 10.5.4 install DVD

MB021Z/A Leopard 10.5.6 install DVD (single user)

MB022Z/A Leopard 10.5.6 install DVD (5-user family pack)

Installing Mac OS X 10.5 Leopard

http://support.apple.com/kb/HT1544

Mac OS X 10.5 Leopard Installation and Setup Guide

http://manuals.info.apple.com/en/leopard_install-setup.pdf

After you install the base 10.5, download & install the 10.5.8 combo update at http://support.apple.com/downloads/Mac_OS_X_10_5_8_Combo_Update

 Cheers, Tom 😉

If you own and plan to sync an iPad or iPhone, after installing 10.5.x it will require an update to 10.5.8.

iTunes 10 requires > current version of Safari > requires 10.5.8.

Mac OS X 10.5.8 Combo Update:

http://support.apple.com/downloads/Mac_OS_X_10_5_8_Combo_Update