Well, lets see what the FSM says:
For "vehicle doesn't move in any forward or reverse range"
Manual linkage out of adjustment
valve body or primary regulator faulty
parking pawl faulty (doesn't fit for your symptoms)
torque convertor faulty
convertor drive plate broken (doubt it would work at all then)
oil pump strainer blocked
transmission faulty
For "slips on upshifts or slips and shudders on acceleration"
Manual linkage out of adjustment
Throttle cable out of adjustment
valve body faulty
transmission faulty
Those are the 2 detailed "problems" that seem to fit with what you've described.
I would check to ensure the linkage from the selector lever is adjusted right (push the thumb button and find drive by feel rather than the detents in the shifter lever, does this make the tranny behave properly). You said the kick down cable was changed, when was this done relative to the onset of symptoms? Is it adjusted nice and tight? How have the shift points been since it was changed?
Other than these ideas, the only other thing I know of that you can do short of tearing into the tranny is the "party trick" governor flush, but a poorly behaving governor would effect the timing of the shifts, not engagement as far as I know.
Hopefully you'll get some more feedback from others tomorrow.....