Why won't my 1998 automatic transmission dodge neon shift into third gear?

Automatic transmissions work on a combination of fluid pressures and electronic signals. Make sure the fluid level is proper, and does not smell burnt. Burnt fluid can be a signal that discs are slipping in the transmission. Also check to see that the linkage is tight and set properly. An unadjusted linkage can cause the transmission to not go into the proper gear.