WHICH PowerPC G3?
Is it a blue & White G3 tower?
Or an iMac? There's 6 different models in two generations that all have PowerPC G3 processors...
Or a PowerBook G3 - there's two different models that can run at least 10.3 - and also have PowerPC G3 processors
Or an iBook? 5 or 12 different models (depending on how you count), all with PowerPC G3 processors.
Or, there's also the old Beige G3, with a tower, or desktop, or an all-in-one G3 (forerunner to the first iMac), all also with PowerPC G3 - and can be upgraded to 10.4 with an upgraded replacement processor.
On any G3 Mac, the amount of RAM memory that you have installed can be the biggest factor in running an updated OS X version. 512 MB or more is great.
The page that I linked to is the combined updater for 10.3.9 - and not the "entire operating system"
The combined updater, for each major version of OS X over the last 10 years or so, is often used as a good troubleshooting step to fix up odd issues that might start happening in OS X. It's not a 100% sure thing to help, but I have seen that updater help many times, and can fix your issue. The reason is that the updating script in the update verifies that all files provided by ALL previous updates, are in place, and properly set.
Because the update includes ALL updated files, they get pretty large. The one for 10.7.5 is over 2GB, for example.
And, because it is not a sure thing, then a very slow download might, in the end, prove to be a wasted effort (but still worthwhile to try)
But, perhaps you have access to a faster connection somewhere? You could download the update through a different computer, and copy it to a flash drive, or whatever you might have for portable storage.