Sir Charles:
You've done all the right (logical) things. If it won't move with the key turned to on (all the warning lights come on but not cranking the car), then the only thing I can think of is that the spring is broken in the shifter handle and it is jamming the button. Before you do what I mention below, run a search at TCCoA.com, the T-Bird & Cougar site -- the folks there have had plenty 'o trouble with shifter buttons sticking and have figure out the best ways to fix the various problems.
OK, if you don't find anything helpful at TCCoA.com, then it is time for surgery. There is a tiny allen screw in the front of the handle. You can feel it, just under the tee branch where the handle begins to taper and it is right in the center. First, remove the trim cowl by pulling it up (gently) to expose the shifter base and OD wire. Feel under the base and try to disconnect the OD wire from the connector. It is a pain. Next, you'll have to manoeuver an allen key in there and, once it is loose (don't take it out all the way or drop it), gently pull up and twist the handle. Don't yank up too hard or you'll snap the OD wires (they are very thin). With the handle loose, you should be able to see if the button in the handle is stuck or if the white button on the top of the shifter is stuck. Either one of these will cause the problem you are experiencing.
HTH,
Chris
edit: lol, I just read your 2nd post. I think you've found the real problem. So, .... nevermind... ///end of edit
