The fob uses a rolling code so if a button has been pressed too many times when the car can't receive the signal for whatever reason, the fob and the car are out of sync. On a ;later car it should resync automatically but it doesn't always work. To sync the key, put the key in the door lock, turn to lock, hold there, press and hold the lock button on the fob until the LED flashes faster, release the fob button then turn the key back to centre. Then repeat only turning to unlock and holding the unlock button on the fob. That should sync the fob to the car again.
To enter the EKA, you turn the key in the door lock to lock 4 times. On each turn the hazards will flash. Then turn to unlock to enter the first number. So if the first number is 3, you turn to unlock and back to centre 3 times, for the second number, it's turns to lock and so on. If, after entering the last digit, which will have been turns to lock, you then turn to unlock, all doors will unlock and you know you've got it right. You have to be slow and deliberate with the turns, a second a time works well.
I repeat, you CANNOT turn off the immobiliser. If you could, the car would never have passed type approval when it was new as all cars after sometime in the mid 90's (I could look up the exact date but can't be arsed at the moment) had to have an inbuilt security system that cannot be bypassed. I know the Nanocom allows you turn turn off Immobiliser but all that does is turn off passive immobilisation but the screen isn't wide enough to fit the text.....
If the car is locked with the key, it can be unlocked with either the key or the fob but if locked with the fob, it must be unlocked with the fob. I suspect while your car was away they were either locking it with the key or just not locking it but leaving it unlocked but parking inside the workshop.
There is so much bollocks around about the immobiliser system written by people that seem to have no idea how it works, or is intended to work even. Until I retired a couple of years ago, I spent over 30 years as an engineer for Ofcom tracing interference to radio systems, including, with monotonous regularity, interference affecting RAKE (Radio Activated Keyless Entry) systems. Some makes are worse than others but BMW, particularly the Mini, are affected more than most and bear in mind that BMW owned Land Rover at the time the P38 was built. There's two things that cause a problem, a relatively low level signal on the correct frequency, such as a wireless doorbell with the button stuck in, a faulty wireless weather station, an oil tank level sensor where the battery is going flat (for some unknown reason when working normally they transmit roughly every 20 minutes, when the battery is going flat, they transmit continuously) or any other low power device that doesn't comply with the legal requirements of 'Momentarily Operated Short Range Devices' as per IR2030.
The other problem is caused by a strong, local radio signal on a completely different frequency, or, even worse, multiple transmissions on different frequencies. A strong signal will overload the front end of the receiver and desensitise it. Think of it the same as trying to listen to a conversation in a noisy nightclub, you can't hear what the other person is saying because of the loud background noise. This is why you can get a problem if parked close to a transmitter site. Usually all you need to do is put the fob next to the receive antenna in the RH rear window, thus making the fob signal strong enough to drown out the other signal. BUT, if you have already been poking the button multiple times, then the rolling code will have rolled too many times for the receiver (well, strictly speaking, the BeCM, as the receiver just passes the received code to the BeCM) to be in sync.
Being close to multiple transmissions gets more complicated as we are then into the realms of internally generated intermodulation products but I'll leave that explanation for another day.....