Wont shift out of first gear

SOURCE: stalls when put into gear

Its possible it could be other things causing the problem, but seeing as you've checked most of the likely causes, it is most likely your Torque-Converter. The lockup clutch in your Stator-Fan located inside the Torque-Converter could be siezed, causing the car to stall.

SOURCE: 1995 crown vic gear problems/gear shift wont lock

if the shifter is loose and sloppy feeling then the shift cable bracket has come loose under the dash at the steering wheel. remove the lower panel under the steering wheel so you can see under the dash then get flash light and look while jiggling the shifter. you should be able to see the cable and bracket. if the bracket is loose then tighten the bolts. note this bracket is at the steering colum.

SOURCE: AOD trans wont shift when cold

Ok I have no Idea who told you not to change the fluid? However there is a reason you have to drop the pan to drain it, or change filter and the reason for this is. So you cant just change fuild and leave dirty filter in, or change filter and leave dirty oil in. Your wouldnt just change one or another on your motor would you? lol Anywho your problem is either burnt fuild. Yes the fuild can be come burnt and lose it vascoity, and weight. (basicly your runing gravey through it.) lol Or the fuild is termendously dirty strained or not. FYI there are clutches in your transmission.... Have you ever heard of clutch dust? Well in an automatic because of the fuild its not clutch mud..... explaining why when its cold and the oil is super thick it has problems, but when it thins up when its warm its fine.

CHANGE YOUR FLUID & FLITER

SOURCE: won't shift out of first gear

good diagnosis that is correct if the vehicle speed sensor is not working the speedo doesnt work and the trans doesnt know when to shift

Testimonial: "EXCELLENT"

SOURCE: auto transmission slips then grabs

first thing i would try is changing the transmission fluid out and filter, i beleive its almost 8 quarts. use a full quart of lucas transmission additive with the new fluid. if this doesn't help, the transmission will either need replaced or rebuilt