I'm having the same issue, exactly as you described it. My fear is that our iBook g4s are simply old creatures. I had bought mine refurbished in the fall of 2004 (4.5 years ago.) I'm not sure when Appple introduced the G4, but there's a possibility my model could be that old. After all, the iBook is not a MacPro G4 tower. But here's to hoping that the HD on the iBook can still be found, since we both probably have some data on our drives that we need to salvage.
Here's some backstory: About 8 months ago, just before my Applecare protection was about to expire, my iBook G4 froze up during normal operations. When I restarted it, I got the gray screen. Occasionally on different start-ups the computer would cycle through red, green and blue screens. I spent some time on the phone w/ Apple's tech support (great folks), and we ran through some tests (which I can't now recall). They told me it was likely my logic board that needed replacement. Luckily, the applecare plan was still in effect, so I just brought it in to the nearest certified technician, and everything was taken care of, free of charge. I had a fully functional iBook g4 on my hands.
That is, until October or November, when I was importing some video through the G4 to an ext. HD. The playback screen on iMovie got all glitchy -- no other part of the screen, though -- and iMovie "unexpectedly quit" (Applespeak for "crash," anyone?). Same thing as last time, but now no AppleCare. Cut to three days later when I try, out of sheer desperation, re-starting the iBook: IT WORKS!
And things were pretty fairly well like that up until now. I probably shouldn't have kept working on the machine, which I realize now. But shelling out another 900 to 1200 bucks for something that could handle the kind of video editing I need to do just hasn't been feasible. So I kept working on it while backing things up on an external HD -- which is now also wonky, vis-a-vis its performance w/ my wife's 526 MB RAM 1.8 gHz MacBook. (Not the best RAM/processor to be trying to regularly edit video on as well, I realize.)
So -- now my advice, belated because I needed to just get that whole ordeal off my chest -- if you've got applecare, use it. You might get 3 months or 2 more years out of your machine. If you don't have applecare, your options seem to be as few as mine are now.
Find a local tech shop that can install a new logic board for you. Not sure how much that's gonna cost, though. You might also locate your local college's computer science club. Ask if they can find you the right logic board and install it for you. If this works, and the harddrive is recoverable, I would suggest purchasing an external HD and saving everything onto that machine when you work. That way, a crash is not such a big deal -- you know, aside from not having a computer to work on.
But, if it's irreparable, you'll have to bite the bullet and purchase another computer. From my perspective, this G4 has been through a lot -- I've put a much heavier workload on it that a laptop should really be asked to handle. And it served me well the last four and a half years, especially for being a "new-to-me" refurb-ed model.
See if either the shop or the CompSci club can salvage the data from the HD. I'm guessing you and I are both out of luck here, as the install disk isn't reading any hard drive whatsoever.
Sorry to be the pessimistic bearer of bad news, but I'm of the opinion that iBook G4s are an endangered species. If you can get around some of the technical problems now or simply retrieve your data, you're probably best getting a newer model.