Sounds like your Battery was already old, not sustaining charge over 3 weeks. On top of that, when you completely drain you battery it can get damaged further. What you describe sounds like that.
I had the same behavior with my Toyota Aygo a while ago. The battery could not stand the load of the starter motor any more. Changed the battery and all is fine now.
(My Mechanic called it an "internal shortage", read about it here)
I suggest you replace the battery, should be a lot cheaper then spending £200 on finding nothing and actually solve your problem.