2002 caravan intermittent problem

My Dad just called. His 2002 Caravan has been behaving bizarrly.
It will generally start normally, but then immediately stall. It will
restart this way several times - and then sometimes run fine. Other
times after several restarts the lights on the dash come on, but it
will not crank - not even a solenoid click.

Walk away from it, and come back in half an hour and more likely than
not it will start and run perfectly. Then stop somewhere, and try to
start it again in five minutes or so - good luck.

The ignition switch has been replaced, with no change in behaviour.
Has anyone run across this before? If so, what was found?
I'm thinking a bad ground somewhere is a possibility.
It only has about 68000 KM on it - out of warranty by time.

Any experience with this problem (Caravan 3.3 - not a Grande)
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