Not sure what to recommend. Aftermarket systems can be difficult to troubleshoot. Doesn't help that the installers often use poor connectors (Scotchlok) that can fail over time - allowing in moisture, for example. Typically the troubleshooting these aftermarket systems is to remove them but if believe the system is good, I'd test and likely undo/redo each connection.
Aftermarket systems are a pain in the arse to troubleshoot and made so more by the fact very few people have a schematic for them. And yes, those damn scotchlock connectors should be outlawed especially when using outside of a vehicle's interior in the weather a vehicle can be subjected too especially in areas where it gets wet a lot.
First I would ask has there been any work done on the vehicle just before this happened? Installation of any items, replacement of any factory or other aftermarket items.
You have checked all the fuses (factory and those installed for the alarm system)?
And, most aftermarket alarms systems (at least the ones I have seen or had on my vehicles.....Viper and Python from Clifford Electronics) have an ignition bypass switch hidden somewhere, usually, under the dash within easy reach of the driver. It is used to bypass the system if you don't have the remote, or the system is set off. You can try that; however, that is temporary and not a permanent solution.
My suggestion goes along with alrock, but to help the troubleshooting, you really need a schematic for the system installed. And many of the systems only distribute this info to authorized installers.
If no schematic attainable, and even with a schematic, there are some circuits I would look at first for bad connections. (Info supplied based on a 2006 H3, and it may vary VERY slightly in later years....NOTE: Might want to add your vehicle, year, etc., into your signature for future questions...it does help).
Look for purple wires into the BCM on a 2006 they will be located at A41, A42, A47 BLACK connector. A38, A39, A44, GRAY connector; both connectors on BCM. Pin 2 on Data link connector directly under the steering wheel use for the scan tool and other nefarious reasons.
And also, don't forget to check the grounds for the alarm system computer.
If these connections are ok, time to just search and check all wires from the alarm system computer.
