There are two of varieties of iMac G3. If you have an original (M4984 with tray loading optical drive), your only option with a broken optical drive is to put a hard drive in another PowerPC Mac of a similar vintage and run the installer on that. Then transfer the drive into the iMac. These iMacs cannot boot via USB, and do not have Firewire. The optical drive and HDD are the only way to boot them.
If you have a later iMac G3 with a "slot loading" optical drive, you could boot the iMac into Firewire Target Disk Mode, then run the Mac OS installer on another computer connected to the iMac via Firewire. This still requires another Mac that can run the installer, and a Firewire cable. These iMacs can also boot from Firewire if you were somehow able to burn the installer to an external Firewire HDD, but most of us don't have something like that laying around.
I would try two things:
- Re-burn your boot disk. If your source image is a .ISO or .TOAST file, you should be able to use any popular burn tool (on Windows or Mac) to write it to a CD. I've used ImgBurn on Windows for this with no issues in the past. If you're using some blank CD's that have been sitting in a closet for 20 years, try to track down a fresh one since this media does go bad over time. Also, some older Macs can be funky about reading CD-RW media, so if you have access to blank CD-R disks, use them instead.
- Install a replacement optical drive. Once upon a time there were a lot of iMac G3's in the wild, so parts aren't too hard to find. iFixit has repair guides for the tray-loading models, and a teardown for the slot loading models.
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Here’s the specs of your system iMac G3/233 Original M4984)
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