Three things struck me a few moments ago (sorry). You said it made 'the right sounds' when booting, it showed a question mark, it acted as if it slowly went into sleep mode and wouldn't come out.
Beeps & flashes when booting
That may not be a hardware problem, because there should be (if I remember correctly) a diagnostic beep pattern if there is no keyboard, and most likely if there is no monitor on a laptop). Unfortunately, I can't find a list of these. Others can. When booting, listen for unusual beep patterns and patterns of flashing LEDs on the top edge of the cover (when closed). These can tell you what hardware is malfunctioning.
EPROMs
The PRAM controls the question mark (where's a bootable disk?) and the PMU chips control sleep mode. Each can be corrupted by a discharged PRAM battery or power fluctuations (vacuum cleaners running in the house).
I was under the impression that the G4 iBook had no battery, and the values were copied anew during each boot. However, this document suggests otherwise. Try removing your Li-ion battery and using the wall cord, just to be sure you're getting enough power. If doing this changes any of the things listed below as stored in PRAM, you may not have a battery.
Mac Family Batteries
http://support.apple.com/kb/HT2295
What is Stored in PRAM?
http://support.apple.com/kb/HT1242
Because the Power Mac has individual parts once can test, I just checked what Apple does when they have similar problems:
Power Mac G4: Screen is Black, Startup Tone Present, Drive Operates
http://docs.info.apple.com/article.html?artnum=95055
Power Mac G4: No Video
http://docs.info.apple.com/article.html?artnum=95043
Finally, I found this:
Troubleshooting Portables that Won't Turn On
http://support.apple.com/kb/TA25686
Sadly, it says nothing of bleeps & flashes.
Each of the above start by recopying the PRAM and PMU from ROM chips. However, you may wish to look for one of these symptoms first.
When should the SMC or PMU be reset?
http://support.apple.com/kb/HT1894
Resetting PRAM & VRAM
http://support.apple.com/kb/HT1379?viewlocale=en_US
Resetting PowerBook and iBook Power Management Unit (PMU)
http://support.apple.com/kb/HT1431?viewlocale=en_US
Sometimes pressing 'C' just doesn't boot the CD. (I think it wears out.) Try holding down 'Option' instead, for a list of bootable drives. Hold it down long enough. Did your computer come with something like this (that came with my G3 iBooks)?
Apple Hardware Tests on CD
http://docs.info.apple.com/article.html?artnum=112432
If not, there's the Apple 'Genius', or a LiveCD Linux. Even the Intel version of Linux that boots on Windows machines has some tests for PPC machines, and can test the partition table & file system on an HFS+ disk. The 'Apple Hardware Test' is the way to go, though.
If your drive has logs of its failed boot, Apple would have read them. I have lots of ways of reading them, if they forgot. Others will have more. Just write back.
Also, your hard disk has early partitions with basic device drivers, necessary to boot. Presumably a CD has these, and a scratch would be bad.
Look & listen for beeps & flashes. Nothing out of the ordinary means, I suspect, a firmware or software problem. Someone may know of a list. Good luck!