Could be the alarm and immobilizer together are causing this. I agree that you need to check the dash wiring-was there a previous owner who installed an aftermarket alarm or stereo in the car-the harness will have evidence of these.
Honda does a great job with their design work. Parts can fail. You do not know the entire history of the car if you did not buy new and that is also part of the problem here. Could be it was very wet at one point-if it came from another state like Texas after a flood. Go over the car including pulling the door panels and checking all of the switches for moisture and corrision. Did you do a CarFax before buying?-that will also be a help.
One other thing--get a Helm manual. All of the wiring is in it.
Hope this gets you on the right path.