If the engine will not crank over, the most common problem is the starter. These will tend to go out at about 100,00-125,000 miles. Sometimes it is only the starter solenoid, but often the complete starter (including solenoid) needs to be replaced.Google+
Car Problem Reports
Toyota Previa Vehicle Won't Crank Due To Starter
Toyota Previa Problem
Visitor, 1993 Toyota Previa, 220,000 mi
Starting when this vehicle was 3 years old, it periodically will not start - no sound, no turn over of any sort. This never occurs with a cold start. Tends to occur when vehicle is warm and/or after it has been parked on a hot day. Impossible to re-create at a shop. Replacing part #8591030050, a RELAY ASSY, CIRCUIT seemed to help for a few years. Generally after the vehicle has sat for 1 - 3 hours it will start normally.