Why does this mac keep going to sleep?

Are you sure about the "sleep" mode ?

or does it switch off ?

or the screen switches to black (the light goes out) ??

did you try to boot it from the optical drive ??

There's a switch in the hinge that tells the machine when the lid is down. When that switch closes, the machine goes into sleep mode. The Wallstreet dissipates a lot of its heat through the keyboard, so this is a self-preservation feature - running it with the lid down would fry the boards. If the switch is stuck (which could well be the case given the broken hinges), then there'd be a constant "lid is closed" signal, which would produce exactly this behavior.

Disconnect the power, remove the battery, and carefully open the lower case to get to the hinges (I believe there's a teardown photo set for the Wallstreet around here somewhere). Locate the switch and check it with a multimeter to see if it's working. If it's stuck, you could just disconnect it and tell your little brother to avoid closing the lid or covering the keyboard.

In your troubleshooting, did you happen to reset the PMU? It controls the sleep functions. Just a thought.

PowerBook G3 Series (M4753)

1. If the computer is on, turn it off.

2. Simultaneously press Shift-Fn (function)-Ctrl (control)-Power.

3. Wait 5 seconds.

4. Press the Power button to restart the PowerBook computer.

A hard reset might work if this doesn't. Remove the battery, then hold down the power button for 30 seconds. Wait five seconds. Replace the battery and push the power button.

I'd just like to thank @rj713, as your "another possibility" was the correct one for me. I recently acquired a Wallstreet in extremely good quality because the hard drive broke down early on and was never used after that. So I replaced the hard drive, which triggered this glitch with regard to the sleep switch.

After I held a small magnet next to the case for a few seconds, I was able to finally wake my computer from sleep. My mouth fell open from surprise. Didn't expect it to work, but it did. Thanks!

edit: in case the original link goes down: replacing the hard drive might generate a magnetic field that's slightly too strong for the Wallstreet's design. When you close the cover while it's on, it will not wake up from sleep mode, and if you close it after shutting down, it will not start up. You will hear an "electronic clicking" sound when you press the power button. Resetting the PMU won't help. Simply holding a regular magnet (I used my MagSafe 2 converter) against the case next to the delete button can 'reset' it.

My 233 mhm G3 is the first generation.

The PMU board is located on that model to the LEFT of the track pad as shown in the “Service Source” Manual. So I placed a screw tray magnet right about that and I was able to get it running!

Mine would fall asleep boot after it reached the desktop.

I bought a new hard drive (40GB) after the last one crashed. It worked fine before that. I also made a new back up battery from separate cells I bought off eBay, but that is a different story.