Can't estimate what the odds are, but download the 10.4.9 Combo Update. Install over top of your current Tiger 10.4.9 system. It won't duplicate, only MIGHT fill in what's missing, including AirPort items.
Use the utility "Disk Utility" (First Aid pane) to "Repair Disk Permissions" before and afterwards. Also verify disk and repair if necessary. Open "Help" menu while in Disk Utility to learn more from Disk Utility Help, or check out this article:
http://www.thexlab.com/faqs/durepairfns.html
In addition, some have had success restoring normal AirPort operation by (in Tiger) replacing their preferred network. Best to delete ➖ your network at AirPort/AirPort pane of Network panel of System Preferences (in the "By default, join:" selector when it's set to "Preferred networks"), then click "Apply Now" button.
Restart Mac. Check in the menu bar icon that AirPort is turned on and that your network name is showing, but is not connected. If so, add in your network using the + box under the list, then click the "Apply Now" button. Switch to Show: Network Port Configurations, put AirPort at the top of the list, all boxes can be left checked. Click "Apply Now" button. Should connect.