neutral safey wire

I was wondering if anyone can explain the purpose for a neutral safey wire. My guess is that when this wire is hooked up to the alarm system, the alarm caan sense when it is in gear and will not let the car remote start.  The reason why I am asking this is because my key will not come out of the car cylinder.  Someone told me the key is stuck in the cylinder and needs to be replaced, but some thing tells me its not that.  In order for a key to come out of the cylinder, the gear has to be in either park or nuetral, otherwise the key wont come out of the key cylinder, I want to know if a wire is loose somewhere in my vehicle which is causing the car to think the car is not in park , hence, not allowing the car to release the key from the cylinder.  IF this is the case, what wire and where might i look for to check this, the car is a 1998 isuzu rodeo 2wd.  Thanks ......

Its probably not the neutal position switch. If it was, you wouldn't be able to start your Rodeo by key. Its probably the key cylinder.