98 cavalier brake problem

I have have a 98 cavalier. If I am driving slow and apply the brake it will sometimes make a noise and have trouble stopping. This only occurs when the abs light is off and the car is going slow. When the light is on, it stops fine and doesn't make the noise. The noise is almost a grinding sound but kinda pulsing like the abs is trying to work. Replaced the pads and rotors but still have the problem. Any ideas?

maybe something screwed up with the ABS??? sorry I'm not much of a help on this but im just trying to help you narrow down your problem.

Got the same problem on my '99 cavalier. Had the ABS system looked at but will still do it, occasionally locking up the tires when braking at low speeds. Strange. If anyone has any ideas please let me know!