It's actually a 4 spd Auto [1st ,2nd ,3rd ,OD or 4th] called the A604 [tranny code] unless you or someone else has done a rather impressive swap.

To me it sounds like you are in limp mode.

There are a few questions you need to answer. I only remember a couple. There are others with more knowledge on here that would know the rest.

1: Did you recently put any transmission fluid in?
   If you did, make DAMN sure it was ONLY Chrysler ATF+4 Automatic Transmission Fluid. The A604 will have a heartattack if you DON'T!!
   This is available at any NAPA, Advance Auto, O'reilly's, Murrays, or AutoZone.
2: When was the last time you changed your filter?
   For the correct fluid type refer to question 1. An Auto Trans Filter should be changed at the LONGEST, every two years. If done properly [and i do stress that],
   there shouldn't be any problems that weren't already there after it's done.

Now the A604 is [co]controlled by it's own computer and talks constantly to your main computer. If there is a breakdown in communication that could cause a problem. I'm going to guess but i'd say you have a V6. Every V6 was Auto. [Hopefully] The 5 spd swap is actually being worked out and on as we speak. If Alain posts in here it should be more beneficial for you. I don't know how much transmission experience Mcgyvr has but he might also know.

Your car is most likley in the fail safe mode and remember if you end up needing to add oil
#4 oil  wasnt used in 95 so I dont recomend mixing because I dont know the out come..proubly none .
However ck on that,  we use mercon 3 and 4  in the units,, their  tons of hot air and not
much fact out their because people say things but they do no research,, The #4 oil is
mercon 5 and deals with heat on a much better basis and we use it in the ford  power
stroke units also  however for years we used dextron 2 in the 604 and just to end the hot
air I build one of my 604 race units and used the cheapest dextron 2 I could get and
guess what, It works fine and Im still beating the hell out of it,Their is more hot air out
their than fact when it comes to transmissions and I always got some morons who know
nothing and dont work on transmission telling you your wrong , they have lots of
entertainment value but not much else...If you have transmission questions, go to a
shop or ask a transmission person... Roger reynolds.. owner  Hannibal transmission
and roadrager quick change gears... go ahead and change both input and output
and dont buy them at auto zone,, go to mopar.....I can give you the ins and outs
on the reasons for different oils but I dont l have two days to wright a report
E   RREYNOLD@NEMONET.COM  roadrage quick change gears...

Mcgyvr, I don't think i can smile any bigger right now. thank you.

Thanks a lot for the help .  Im just hoping its some electrical problem and not something more pricy.

Shiano, the fluid I added recently was ATF 4 , but honestly I dont remember when was the last time I changed the filter, so that should be my next step. Its a 4 cylinder by the way. Thanks
Ill update the forum once I get the problem fixed.

Just make sure you remember. 

Can you get your hands on a scanner and ck for codes. With scanner ck input RPM in park, should have engine RPM and ck the output in drive or reverse and let the car roll or drive in parking lot. You want to see RPM from the sensor too. If you don't have any RPM from the sensors, ( Zero ) the sensor that reads (Zero) is no good. Just for information if you already replace the output and still reads zero, then you have a broken wire at the connector. If the sensors read good, then you have inside the transmission.

if you're in the midwest-east coast you can go to an Advance also.