If you can afford a subscription to alldata you will have at your finger tips all the information you and we need to help you figure this problem out.
BTW I have never seen a aftermarket alarm system professionally installed.
Every time I have encountered an alarm system it is accompanied by a rats nest of wiring that doesn't get trimmed down properly and zipped tied under the dash.
These professionals splice into the factory wiring using scotch lock connectors like in the link provided.
http://www.amazon.com/3M-Scotchlok-Electrical-560B-BOX-Retardant/dp/B0002BFZ8E
They also normally cut some of the factory wiring in two, splicing in much thinner wires from the Alarm harness with crimp connectors.
Then they ball up the rats nest and zip tie it under the dash.
I hate this type of work and connectors with a passion.
A professional job each and every connector would be soldered in place and heat shrink tubing plus electrical tape is used then these wires would be protected in a wire loom.
the wires would be routed in such a way that it flows with the factory wiring harnesses.
To date I bet I pulled out over 200 Aftermarket alarm systems and each of them was installed by the same type of commission minded rush through it type of mechanic.
So my point is you would be doing the car and you a big favor by taking your time with the battery disconnected, pull the lower dash pad off and removing this wiring nightmare
out of your car. and re solder and restore each wire the way it was when it left the factory.
Even if this alarm has nothing to do with your problem, I would remove it.
Yet this is your car, you invested the money to have this done, so it will need to be your decision to remove it.
Your car has a circuit that will interrupt the fuel pump when the car is running and reports low oil pressure, that small relay may have something to do with this oil pressure sending unit.
I am willing to bet that the orange wire with black stripe can be found near the fuel pump, jack the car up and see if you can locate it, probe the wire with a test light when someone turns the key on it should have power for 2 seconds or so, when cranking the wire should have power on it the entire time the car is cranking.
If you have power the fuel pump needs to be replaced.
If you do not the car will need to be diagnosed using the information found in the manual or online at alldatadiy.com we can help with those test if you need it.