a weird phenomenon with a 12V black & decker cordless drill
Battery powered power tools cannot possibly "run well" from a PC power supply. The reason is that PC power supplies usually have certain cut-off threshold in current supply, and will  disengage abruptly when heavy loaded. Power tool motors, unfortunately, have very low impedance when stalled (and started), which require peak currents in 30-50A range, and PC PSU just cannot handle this. Your drill might start, but any serious load will lead to "shaking and stopping". Compare your problem with this one, How many amps does a 18v cordless drill draw?