Hello, the last version of iTunes foe Tiger/10.4.11 is v9.2.1...
Safe Boot, (holding Shift key down at bootup), run Disk Utility in Applications>Utilities, then highlight your drive, click on Repair Permissions, reboot when it completes.
(Safe boot may stay on the gray radian for a long time, let it go, it's trying to repair the Hard Drive, & clearing cache files.)
Open Console in Applications>Utilities & see if there are any clues or repeating messages when this happens.
Try opening iTunes.