Check the house alarm's power source. Most alarm systems operate both on direct hard-wiring and batteries. The batteries act as a backup should power be disrupted or go out. Open the battery compartment and replace the batteries. In addition, check the wiring running to the electrical outlet and alarm panel. Inspect it for breaks or burn marks.
Check the sensors. Door and window sensors are activated when the system is armed and the door or window is opened. Set the alarm to its "armed" state and open and close windows and doors one by one. If one or more sensors does not trip the alarm when armed, those sensors are faulty. Check the wiring going to each faulty sensor or replace the battery if wireless.
Test the motion detectors. Arm the house alarm and walk past the motion detectors to set the alarm off. If the system does not respond, the motion detectors are likely faulty. Contact the monitoring company or the alarm installer and ask to have the motion detectors replaced.
Attempt to resolve the problem by resetting the house alarm. Systems will differ by manufacturers and models but in general, the system is reset by using a paper clip or needle and depressing the "Reset" button. On some systems, resetting is accomplished by disarming it, removing the batteries and shutting off the wired power source.