Here's what you should do:
1. Drive cautiously: The ABS is malfunctioning. While you can still drive the vehicle, braking distances will be longer because you're relying on standard braking instead of the ABS's assistance. Avoid hard braking.
2. Get the ABS system checked: The "Check Anti-lock" light indicates a fault within the ABS system. This could be anything from a faulty sensor (wheel speed sensor is common) to a problem with the ABS module itself. You'll need a mechanic to diagnose the issue. A simple code reader might be able to help determine the problem area, but a proper shop visit might be necessary to replace parts.
3. Don't ignore it: Continuing to drive with a malfunctioning ABS is risky. The sooner you have it addressed, the better.
In short, the engine starting isn't directly related to a security system problem; the ABS light is a separate issue requiring attention.