The disk utility runs forever and then reports that it can do nothing.

Is there a work around?

What is the prognosis for this older laptop which otherwise works?

Disk Utility dose not scan the whole disk. There are files that can not be scanned because of permissions issues. There are third party disk utilities and ways to use disk utility to work around problems with Disk Utilities
If you have a second Power PC based Mac ruining OS 10 you can use Apple Disk Utilities to check the drive by booting the powerbook while holding down the “T” key. This effectively turns your Powerbook G4 into a Firewire drive. Connect your Powerbook to another PowerPC based Mac and run the Apple Disk Utilities program on the hard drive of your laptop from the other computer. This allows access to more files by the application.
Disk Warrior is also an option. This program works and is part of my kit (I support 200 Powerbook G4s) it is a bit pricy for the average user at $99 but if you have mutable Macs it is nice.
A third option is to reinstall your system and software. Backup your folder under users to an external drive and reinstall. Set up your user account on the Powerook exactly as before , same name and password. Next you will need to install all your applications and run updates. After these steps are done you can copy your backed up home folder into the new install while logged in with your login. When done properly everything will be there all settings and tweaks applied.
Printers and wireless profiles are in the Library folder in the root folder and not in the user level Library folder. Do not copy these folders over it is a easy way to ruin your new install. You should add the wireless and printers manually

Thanks so much! This is similar to advice I got elsewhere last week, including Disk Warrior. But your answer is much more complete and organized.