Compatibility of iMac G3 hard drives, to try to recover data
Well, while newer iMac drive will work in older one, there is no guarantee it will boot.

There was a limitation during the times of Classic Mac OS on size of boot partition which has to be below 8GB. You have Mac OS X 10.3.9 on that drive so I can't say if it still applies. And maybe if it does apply you might had it partitioned just the way it need to be to overcome it.

Then again getting HDD from that iMac and into it is not that easy. Not that it really hard but still it is not a Mac Pro or standard PC case.

And also keep in mind that you might just break cables when disassembling since it is long time when it was put together and they probably aged and aged cables don't like when you bend them.

So if you are not afraid of the idea of making another iMac unusable or brave, experienced or just curious then go ahead and try. Do not forget to remove power cord, then press power button to get excessive electricity from capacitors off and get yourself grounded.

Still there is an option and it is just buying a used (they are cheap since practically nobody use them) or getting for free a USB enclosure (it could be USB 1.1 or USB 2 — it doesn't matter since that iMac only has USB 1.1 ports anyway yet USB2 enclosure will work too. It even can be 5.25" external CD case provided it internally uses PATA/IDE interface) case for 3.5" PATA/IDE HDD.

After putting your HDD into it you should see content of it. Provided it is not dead, of course.

So good luck and keep us posted.