The 12V battery needs to be charged else you get some strange lights. The issue is that although the dash will light up there may no be enough 12V power to trigger the relays and speed controller.
Check the 12V battery Voltage. Full will be around 12.7 volts and 50% 12.2v and empty will be 10.5v but the Twizy needs over 12V. Also needs to be able to supply that under load not at rest.
ie. checking a 12V outside the car may well say 12.5V but under load a cell may fail and the voltage drops by 2v.
How often has the 12V battery left to go 'flat' ? After a couple of times and especially if left flat for any length of time it will never recover enough to be usable. It should be replaced.