I had that same annoying problem with my alarm on my 97 4runner. I just took it out a couple of days ago. Just Take off the dash part under the steering wheel and find the brain to the alarm. Reconnect the ignition wiring so its not "y" to the alarm, or in my case I took the brain out and just cut the 3 wires of attached to the wiring and it had no problems starting, no more alarm!! Or if you want to keep your alarm but just want to get rid of all the sensors going off, just cut the wire under the hood that is the mini horn for the alarm.
Hope that helps....I HATE ALARMS!!