Okay. I spent waaayyy too much time looking for the answer to this problem, so I'm posting this for others in the same situation. I am the Resident Geek at a middle school, and one of our G4 iBooks (1.33GHz) would start up, then immediately go to sleep. If left for a day without power (battery removed and machine unplugged), you could log in before it went to sleep. In all of my searches, including a hint here from 2007, the reed switch seemed to be mentioned a lot...but there was also confusion on its location, and whether the logic board was to blame.
After taking apart the laptop and unplugging the reed switch -- which is located on top of the optical drive -- I confirmed that to be the problem. A new one for $15 (Google it!), and I was back in business. Hopefully this will help others.
Also, I will post the following as another hint, for others taking apart things such as laptops: the issue of leftover screws. The secret to a successful reassembly is the logic behind disassembly. I have found that a rough drawing of the different layers (bottom case, metal shield, etc) with two-faced tape over the drawing to stick the screws to their respective locations does the trick. I know that iFixit has detailed manuals, but given that their manual did not list the reed switch in the correct place, I was reluctant to rely on their screw placement.
Mac OS X Hints
http://hints.macworld.com/article.php?story=20090513063642118