Why would a 1997 Dodge Avenger with a 2.5 V6 and over 120 thousand miles not shift into third gear?

Wont shift?

I had this problem befor also it is your transmission sensor....$20 part $40 for install.....have them do it...then you'll get a warantee on it....

ok there are two sensors one is called input shaft sensor and the other is called main output shaft sensor,, there easy to replace . they are plastic sensors on the front of the transmission . best to replace both cause once one goes bad the other isn't far behind.

however if there is anyother tranny problems internally then changing the sensors wont do you any good tho for the most part id say that's is what the case is with what little information you stated