My iMac G3 DV SE is not powering on after trying to force CD eject

Firstly, let's get rid of that disc. What you found is correct; you can eject the disc using the little hole next to it. However, you'll usually need something longer then an iPhone SIM ejector to open it. Try using an unbent paper clip or something of similar length. After you get the disc out, try powering the computer on. Does it work now? If not, then I would try replacing the battery. Open up the computer (follow this to step 11), and locate the battery. I attached an image showing where the battery is located in the computer.

I'm not sure how the battery comes out; the image isn't high res enough to zoom in and see and there aren't any iFixit guides about replacing the battery. I also don't know what kind of battery you'll need, but Im sure a couple of Google searches will pull up all you need to know. Another thing that may be the cause are the capacitors in the power supply. If those went out, that could also cause the computer to no longer function properly. If the computer is not receiving any power, this could be the cause. Just follow this guide to replace the power supply. You have two options. You could replace the individual capacitors on the power supply, or you could just replace the whole thing. Replacing the whole thing would be easier, but more expensive. Replacing the capacitors would be much harder, but way cheaper. It's up to you, and, again, any information concerning either options is on the internet.

Good luck!