2001 Chrysler Sebring does not shift. I can put it in reverse and drive and it runs, but it does not shift out of first gear. Speedometer still works. Transmission fluid shows that levels are fine.

When you say hesitation do you mean the engine will rev but the transmission won't engage

Sounds like a speed sensor, I will look into that, but if the speedometer isn't working, its either cable, or electronic. Being a 2000, I'm guessing electronic. Chrysler have a lot of electronics on the transmission, as they are electronic themselves. I had an alternator go bad and my battery died, and the car wouldn't shift, it actually down shifted while driving. Have your battery and alternator checked first, then sensors. Like shift silinoid, speed sensor etc.

Check that the shift linkage is connected at the trans, if it is, put some transmission fluid in it after checking the dipstick while running in neutral with brake on.

Drive it slowly to a reputable transmission shop. There is nothing you can fix yourself.

Inspect your shift linkage if it has loosened or misaligned, either at the shifter itself or on the transmission.

run the fault codes to find the reported fault
engine lights report on engines and transmissions
could be actuator or vacuum to actuator, dirty transmission oil or pump pressure problems

Yes. There is a speed sensor that the speedometer relies on, and that the electronics of the transmission rely on. Look into that.

Is the gear shift button stuck in, if so hit the gear shift a couple of time and that should unstick the botton, allowing you to remove your key

If all the gears including Reverse and Neutral show up in there proper place on the shift indicator your problem is either the linkage or the transmission. If your shift indicator is not lining up correctly you are probably putting the car in Second instead of Drive although Drive is showing. See if you can find neutral and go down 1 click regardless what it shows. Then try it. If that solves it, the little needle slipped and it is a simple adjustment to reset it.

have not found the problem yet ---still looking --thanks