Personally, I'd replace the HD myself ... even if it isn't the HD you can probably use the larger drive, or put it in a case for use later.
$50 for a new HD versus $350 for a do it yourself logic board.
Hmmm. I'd likely skip replacing the part and look for the cheapest diagnostic solution... aka, put the internal drive in a case and take it to another Mac.
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Plus, the question mark, and the option restart is working ... if the machine also makes the sound while booting. It sounds like the logic board is working, and the HD isn't -- since the HD doesn't appear anywhere as a bootable volume.
Spending $5-15 on an external IDE notebook USB case for the current drive, and taking it over to another Mac to see if it works is likely the cheapest solution to see what is wrong.
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Remember, a dead HD might work once in 15-20 restart attempts, and either begin booting and succeed or freeze and crash the machine.
Note:
http://www.ifixit.com/Guide/Device/iBook_G4_12"_800_MHz-1.2_GHz
See the iBook G4 12" Troubleshooting Guide .... it mentioning bad HD.
Installing iBook G4 12" 800 MHz-1.2 GHz Hard Drive Replacement
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Besides simple tools and the possible need for a small torx set, all you will need is a plastic spudger tool (the little plastic tool some people may use to scrape off thermal paste) you should be able to pick up at Radio Shack for a couple few bucks.