1996 Dodge caravan V-6 3.0L Engine now cranks up but stalls immediately?

Where to start? Clicking is usually starter related. I know you have a new one, or is it a remanufactured one? As for no power when accelerating, I would tend to think plugged catalytic convertor. For the start/stall problem, take the covers off the steering column and test the ignition switch. It sounds like the current draw may be causing it to heat up and fail to make good contact - fairly common for this type of Chrysler switch.