Why does my car shuts off?

This problem began when the car had problems starting. When I tried to start the car it would seem as if the battery was low in charge and after that it would start and then run normally. So I thought the battery was the problem. After changing the battery the car stated to do this strage thing. It would shut off immediately after it was turned on. The only way to keep it from shutting off is by steping on the gas pedal, if I take my foot off the pedal it would slowly shut off. When I manage to avoid this problem by steping softly on the gas pedal and then switching from "parking" to "drive" I noticed that the same problem persisted if I let go the gas pedal and step on the brakes.
the car has an automatic transsmission.

somebody told me that it might be that the air filter is clogged but I checked that and the filter was fine. Could you please help me. Thanks so much.