[2brits]

My daughters 1998 Neon auto trans jumps into neutral when the gas pedal is pushed hard to the floor.The car has 130000 on it.It is also quite sluggish when accelerating.

 

[Bob Lincoln]

Check the shift cable and the kickdown cable for binding.

 

[ImperialCrown]

They usually bind at the 2 concentric (one inside the other) shafts at the top of the transaxle. They are located behind and below the battery and get misted with acid over the years. Anything located near a battery is susceptible to corrosion.
The shifter shaft and kickdown shaft will bind and and move the throttle and/or shifter together. If the shafts are cleaned and lubed, they should then operate smoothly and independently.
A layer of lube will protect the metal from further corrosion, but the downside is that grease will attract and trap dirt. Both shafts, linkage and cables need to move freely.