My car has 610k on it. In the past months, when I started the car by turning the ignition key; 1 out of 10 chances there is no response. The lights comes on but engine doesn't crank at all. It seems the battery does not have enough power. But when i turn it the second time there is no problem. Any idea on what happened?

610,000 kilometers? That's 380K miles. Not that I have the answer to your problem, but that's a lot of distance for a gasoline car.

Ensure that the DAS isn't kicking in. On my '96, there are green and red lamps in the interior rear-view mirror that alternate when this happens, but yours is a different DAS system. Check the owner's manual. Also see if anything else is noticeable that is out of order. Starting on the second attempt makes it very difficult to track this sort of thing down.

sorry, should be 61k. I wish it could get 610K :-).