Had same problem recently with 93 Probe.  The ignition switch, that is
the electrical part, had failed and jammed.  In my case it also wouldn't
release the key.  I had to have the electrical ignition switch replaced.

If you're lucky, you might just have 18 years worth of crud inside the
lock cylinder finally built up enough to prevent the pins from moving
into place.  I have an 88 Grand Marquis too.  In an act of utter
stupidity, I once got McD's sweet & sour sauce on my keys (made for a
funny story here at the time) and didn't notice until I had shoved the
key into the lock, gumming it up good.  I sprayed a bunch of PB Blaster
(a much better than WD-40 ever thought of being spray penetrating oil
you can get at Wallyworld) in there while holding a rag under the
column.  It came out all BLACK and icky.  You need to bang, wiggle,
jiggle, push, pull, and whack the thing around until you finally get it
to turn to RUN.  I had to let the PB soak over night and then flush it
again.  (Someone else here might have advice about drilling and/or
cutting as a very last resort if that doesn't work.)  Then you can get
the lock cylinder out easily by pressing in the release pin (you need to
take the plastic covers off the column to get at the release pin - you
should really take them off before spraying stuff in there anyway.)
Once you get the lock cylinder out you can see if it's the lock cylinder
or the actual switch behind it that's getting stuck.  AutoZone has the
lock cylinder for $15 with 2 keys and the switch for $12 (you might need
some "security" hex or torx bits to get the switch out though.  I can't
really remember how the switch is held in because I didn't have to
remove mine.  I remember my '93 Voyager had those silly security screws
and I paid more to Sears to get the bits than I paid AZ for the switch
itself.)

Good luck!

--= dj =--