Something like this also happened to my friend's DS, which was also considered a faulty 2nd hand.
One morning he played Devil survivor for around 30mins. Got tired and turned it off. then after around 10-15mins, he opened it up again. Nothing happened. He showed it to me. The "clicks" of the hinge sounded fine. Battery and cart was seated right. I then noticed that during the boot sequence, even though the green LED was lit, no DS chime would be heard. I then told him to have it checked by a pro.
Few days pass. His DS was alive again. He didn't bring it to a repeair centre. He said it just worked fine one morning. LOL