I had the same problem with my 2009 white macbook.
I tried resetting the SMC and it didn't work so I brought it to apple and they sent it to the repair center. It took them 2 weeks to come back to me saying it was the inverter cable and they will have to replace it, it would cost approx. 185 euro. So I said go ahead and do it and a week later, when I was hoping to get my laptop back I received another email saying there was something wrong with the display and it would cost 351 euro.
I was too frustrated and i didn't think it was worth it, which is why i told them to just send me back the laptop.
If anyone has a better idea for a cheaper way to fix it, it would be great.