Exiter wire coming off is a fairly common one. Had that with mine at the start of this year, this wire is a spade connector and the connection on the motor is basically a ring connector over a thread with the spade connection coming off it, and mine was a bit loose and it meant that this ring connection would rotate because of vibration and eventually knock the wire off the connection.I had this same problem today after a somewhat strange turn of events, lol. Early this morning I left for work at my usual time and soon noticed that my only ignition key/ key fob wasn't working and the car refused to unlock. At this point I went back indoors and replaced the transponder battery inside the key but once again upon testing the car refused to unlock. After further examination within the key and removal of the PCB I noticed that the tiny micro switch (which should be securely soldered to the PCB) had a broken solder connection on 1 side, I was then able to quickly unlock the car by simultaneously making the broken connection and pushing the switch at the same time, after this I drove to work unhindered, parked my car and left it unlocked (In a fairly secure car park) While I was at work I had an engineer friend resolder the broken connections and successfully repair me key/ key fob, I thought this was the end of my problems until I tried to start the car to drive home. The doors locked and unlocked fine but the engine would only turnover for 3 or 4 seconds and would not fire at all. After checking for and finding no blown fuses I gave up and phoned the AA. When the AA patrol man arrived he watched while I tried to start it a few times then he looked at a couple things under the bonnet and said try it now, to my amazement the engine burst into life. All he did was pull on what he called the "exciter wire" which connects onto the starter motor somewhere. At the end of the day it's not WHAT you know, it's WHO you know.
One thing I'd say is that if the AA man could so easily see and then get the exciter wire back on it probably means your starter motor heat shield is missing, this is how I was able to keep putting mine back on when it kept coming off. So once it's sorted make sure you get a heat shield for it because this can cause heat related damage being right near the manifold.