This is a very common problem with Dodge Neon cars. They flood in the back seats big time. I had this problem with 1998 Dode Neon (manual), then bough 2000 Neon. Inititially it did not flood at all but now it does. I searched the forms, could not find a solution anywhere. Does anyone know why Neons flood with water in rain?
I wish you luck. In my experience any car that's 10 years old or more is probably leaking somewhere, just most times people haven't noticed yet (although, they eventually notice when the floor rusts through and falls out). The causes of leaks are multitude. You just have to go around every spot where there's a break in the metal (antennas, windows, trim, handles, gas doors, etc.) and inspect carefully/hose down while watching for water...