Broken power button.
After getting it all put back together, I plug it all in, and press the power button. Nothing, and the button seems jammed. No big deal I thought, I'll just take it apart real quick and fix it. Lifting the iMac up, I hear a bit of rattling inside. I'm thinking "Oh, it must be that loose screw I lost. I'll probably need that". I open up my iMac, and see thousands of tiny pieces of plastic everywhere. Turns out, the plastic plunger that goes with the spring (inside the iMac case) to press the power switch, was completely destroyed.
So what now? Should I take to the Apple Store to repair? Though I doubt they'd do anything due to the age of the machine. However, don't iMac G4s and eMacs use the same power button as the old CRT iMacs?
Blue & White G3, Mac OS X (10.4.10)