The door lock actuator *may* have something to do with it. Do you still manually lock that door?
On some cars, a sensor or something gets shot, and makes the alarm go off, since the alarm views whatever it is as "open". I only say that because the hood sensor on the Z32 goes out and gives a lot of people alarm issues.
And as far as removing the alarm system entirely, I'm not sure on exactly HOW integrated the alarm system is on the Murano, if it has a kill switch when you remove it, ect. but the alarm "computer" should be relatively close to the ECU.
Also, here's the link to the Security portion of the Murano FSM, which can be found at
http://www.nicoclub.com/FSM
http://www.nicoclub.com/FSM/Murano/2010/SEC.pdf
Hope this helps narrow the problem down!