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.