I have a 1998 Mazda 626 with a cobra Auto security system. I suspect some problems I have been having are related to this system and was wondering exactly how it disables starting. Specifically one thing I'm wondering is if it disables the injectors somehow or has some way of disabling the PCM.
I'm afraid I have some bad news for you. Assuming that your alarm is a Thatcham approved alarm and was installed by an approved installer, it must disable the vehicle at a minimum of three different points. Additionally the Thatcham specification stipulates the entire alarm loom must be black.
Even if it's a lesser, non-Thatcham alarm, the biggest issue you face is that the alarm provides wiring to disable vital vehicle systems. It is, however, largely up to the installer to decide how these should be implemented and which systems to interrupt. This is largely because all cars are different and implement things in different ways.
Favorites to check are things like ignition systems and fuel systems. A typical installation will disable the fuel pump (assuming it's electronic) and the ignition coil (assuming it's a coil based ignition system). There is no hard and fixed way to install the system or even route the wiring. Reason being; if there was, they'd be far easier to a thief to bypass.
It's a case of pulling trim, following bits of loom, test stuff with a test lamp and multimeter. If you have a manual which contains a wiring diagram for your car, this will help. I'm sorry that this probably isn't the answer you are looking for but this is largely the reality of an older car with an aftermarket alarm.
Having a Cobra alarm fitted to my 1985 Supra, I can confirm what Steve Matthews wrote. The alarm inhibits the ECU (thereby coil and injectors), fuel pump and starter motor. Fundamentally, this is done by intercepting wires going to relays, but a well-fitted alarm will do so in such a way you'd have to dismantle most of the dashboard to find the right wires. The fitting is car-specific. Your best bet is to get a workshop manual and trace the wiring diagrams, look for a likely point to tap into the cables. Fortunately mine has been very reliable.
I had ignition problems a couple of years ago followed up by problems starting. I initially suspected the alarm since it seemed to be the common factor, but they're designed to fail safe. Instead, my problems turned out to be a worn-out relay for the main ECU - the connection was intermittent and almost impossible to trace. I'd recommend checking (or having checked) your relays, as they are a likely suspect.