In reply to d508934:
You're not asking them to investigate - you're asking them to fix it. If investigation is not a specific exclusion to a warranty, it is included. Investigation is clearly included - that is how they now know that they don't know what the fault is. The fact that their investigation is inadequate for the task is a matter for their professional standards, not you. Presumably their line is that if you were to pay for the investigation, they would pay to rectify the fault. However, why should you pay for a service that is both not an exclusion and shown not to be up to the task?
The primary recourse is to be massive pain in the backside, if you seem to have hit a stone wall. A very loud voice in a busy showroom may help. Parking your vehicle to block the entry/exit might also help attract unwanted attention. Tell them you can't move it because the warning light is on...........
However, I do speak having failed to get BMW to pay for an obvious fault. (I hope one of the BMW bots is listening, you feckless little xxxker.) BMW's line was that because they had never seen the fault before, it must be our fault. You may well wonder why neither my wife nor I have a BMW now.