I have read that Lion batteries have a very poor reputation on this forum, so I would not place too much reliance on the guarantee. That's not to say the battery is definitely responsible for the problem, but it does leave a question mark over it.
If you are prepared to take the instrument cluster out yourself and post it to ECU Testing, you should have it back long before your local garages can even look at it. £45 for a diagnosis, about £180 for repair.