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.
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.