Automatic Tranny Shifter sticking

Anyone know the plan of attack on an automatic transmission that has a shifter that is tough to move back and forth. I parked my 2002 Dodge Neon for about a year (outside) and just got it out to change the fluids, plugs, etc. I tried to get it back on the road this past week and the tranny feels like the cable or linkage is very tight. I have never changed one of these before and I am not sure where to begin. It is like this even after driving it for awhile and moving the shifter back and forth a lot.

Additionally it actually seems that due to the shifter being very tough to move it is bypassing Drive and going to 1st or 3rd. Hence while I am driving, it will not shift out of the gear it is currently in. It will shift thru neutral and reverse and these work fine. So it even more so makes me think the cable is the issue.

Finally the tranny or shifter never gave me problems before I parked it this past year. Any ideas would very much appreciated, thanks in advance!

I dont know the steps to removing the shifter cable, but that seems to be what you need to do.
But before that - uncover the top of the tranny so you can drip some oil or penetrating oil onto the shifter assembly where it runs into the top of the tranny. That location is close to being 'outside', and doesnt really get lubrication - other than what might splash up onto the shaft inisde the tranny. Uncovering the top of the tranny will likely mean removing the battery and the battery tray. This is not a hard job, and gets easier after you have done it a few times.
Un-do the connection of the cable to the shifter assembly that is on the top of the tranny - and see if its still the cable that is stiff, or if it is the shifter assembly (lever or whatever you want to call it) on the tranny. If that is the problem, you could use any penetrating oil to get it to free up, then periodically bath the region with something like "Marvel Mystery Oil". Its a nice product that acts like a penetrating oil, displaces water based moisture, and is a thin lubricant too. 3-in-1 oil will also work. I try to do this at least once a year, along with oiling the door hinges, and putting a drop of oil onto the ignition key, then putting it into the lock for ten minutes. Actually each lock on the car.
I think its also possible for the pivot at the bottom of the shifter lever (inside the car on the lower console) to get rusty. You would have to remove the console covers to get to this point - and could try penetrating oil on that pivot as well.
If you dont fix the stiffness, I predict you will eventually need to replace the plastic grommets that support the shifter cable (inside the car & time consuming to access).
A Haynes or Chilton manual would have some explanatory steps, and the Chrysler manual for the car would of course have detailed steps and sketches. I got mine on ebay for about $30. It paid for itself the day the UPS man delivered it to the house.

Thank you for the info. I did exactly what you said. Had to attack it from both sides but I injected some WD-40 in the cable, and also sprayed all around the shift linkage on both the outside (under the battery cover.) And also sprayed and injected it inside the under the center console. Everything is working beautifully now. Not sure if this did it or not but the shifting is much easier. Also it is now properly shifting thru the gears when in 'D'.....not sure if this fixed it or not.

I also changed the tranny filter and fluid tonight, as all the other work was done two nights ago.

Looks like I am going to back on the road pretty soon. Just have to replace a rear wheel bearing, bleed some brakes, and finally replace the mirror on the drivers side mirror.

Thanks again for all the help.

And thank Your for the feedback. By the way, we have replaced the passneger side rear view mirror twice. Once because my son-in-law backed up and knocked it loose, the 2nd time because my daughter backed up (in the same parking spot) and knocked it off. I got the replacements from ebay - cost about $30 each time.