S-320 1995 Starting Problem

Normally, when you turn the ignition key, all of the dash lights above the key light up and the car starts. My cute little conundrum is that intermittently (aarg!) only the SRS light comes on, the rest are dark.
The car will crank, but not start. If I hold my mouth right and play around, it usually starts in neutral. I've tried replacing the neutral-safety switch, but so far no joy. (I've got a cute little quicktime movie of this, if it helps.)
Has anyone got a clue? I've stumped two sets of mechanics so far.

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