On the package the new USB flash drive came in, is there any indication of
which Mac OS X version is supported by the portable storage device?
The latest USB flash drive, such as the Lexar 32GB, is USB3.0 speed
and likely is not backward compatible to USB1.1. So try something less
ambitious for use with the ancient PowerPC iMac G4.
Could be that one is not supported, and since the old iMac may have only
USB1.1 speed ports, to attempt to fill the capacity at that speed would be
super slow. A faster method, if you had correct cabling and know-how,
would be to use FireWire. This may require an adapter for the new Mac
since some of them do not have FireWire ports; so it may require a FW
to Thunderbolt adapter between computers so the files can be moved.
(With that, it may be possible to boot the old iMac PPC in Target Disk Mode,
and move --drag/drop-- folders of images from the old iMac hard drive to
a location, perhaps a folder, on the desktop of the new Mac.)
If you weren't dealing with desktop computers, the Apple Store could have
helped transfer your files from the old to new computer. There is a setup
or migration assistant that can help.
Do you have an externally enclosed hard disk drive already in use w/ old Mac?
To use smaller capacity USB flash drives of compatible specs may work OK
but could still take quite a bit of time to move to/from the chip between Macs.
Is the PowerPC iMac actually running Tiger 10.4.1, or is that 10.4.11?
A difference would mean later driver support, maybe.
Good luck & happy computing! 🙂