The USB port on a PC supplies only 0.5A, so it is not enough to power a fully discharged Zaurus. In those instances, I've been able to charge my SL-5500 from a USB cable with the Zaurus turned off -- it charges at a much slower rate than it would with the Sharp-supplied (2A) charger.
With a partially discharged Zaurus (> ~50%), I've been able to keep the Zaurus turned on and bring it up to full charge off a USB cable.