You said you have been running this on an older machine, so you must have had a Classic environment on the old machine. So you must have had a "System Folder" on that machine in order to run the OS 9 version of HyperCard, right?
From the emergency backup drive that you must have made of the old machine at some point in the past 7 or 8 years, copy the "System Folder" from that to your new machine, and under System Preferences for Classic select the newly copied System Folder. If the old machine has "given up the ghost" and won't run anymore, you may be able to remove the old hard drive, if that still works, and copy the System Folder from there using an enclosure or bare-drive cable adapter to an external port FW/USB on the new machine.
The problem with running on a late model G4 or G5 that can not boot OS 9 itself, is that you can not boot and run any OS 9 installer on that machine. Some of the computer models in that transition period that shipped with Classic pre-installed also came with /Applications/Utilities/Software Restore OS X application on the original OS DVD that would re-install the OS 9 software from the original media DVDs/CDs (at least that's how my G4 MDD worked). Retail versions of OS X do not include the Classic environment or this software restore .app. I don't know if the G5 iMacs shipped with a Classic environment, I'm not familiar with them, do you know how you got it on there in the first place? Was it pre-installed?