Larry,
The way that most ABS systems work, is that they run a system check when the ignition is turned on and if the controller is functioning properly and all wheel speed sensors have the proper resistance, no codes are set and no ABS light is turned on.
When you start driving the ABS controller looks at the output of each wheel speed sensor, and if they do not match without the brakes being applied, the controller will turn on the ABS light because it can not control wheel lock-up unless it knows the exact speed of each wheel.
Under the conditions that you described, it sounds like there is a problem with one of the wheel speed sensors. It could be as simple as adjusting the air gap on a sensor, but it will probably require a scanner that will read codes from the system and real time data to properly diagnose the problem. Unless it is something fairly obvious like a broken wire to a wheel speed sensor or a melted sensor from a badly overheated brake, ABS problems usually require professional technicians for repair because of the necessary tools and experience that is required.
Gerald