The security light is going on because the resistor pellet in your key is either burnt-out or the contacts are dirty, and should be an easy fix. It won't disable the engine if, at some point during the drive, it gets a clear signal through. The logic is that if it stops working mid-drive, you still need to get back home, so it starts the next time. If it gets a signal during the next drive, which is probable due to everything bouncing around, it resets, and although it loses the signal except for that brief moment when it conencts, it waits until the next time it's started to check for the right key code, and the process repeats.
The ABS light may be as simple as the ECU needing a reset after the battery went dead. Mine (another GM car) did that, and not only did the light come on, the brakes locked themselves on and I barely made it to the side of the road.
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