I see a review for this model from June 2010. That's 6 years ago.
I'm afraid repair is more expensive than the current worth of the laptop. So consider replacing it.
All you can do yourself: open the case and check if all cables to the screen are fine. See https://www.youtube.com/watch?v=YumiMlucrUY on how to do this.
I have a dell inspiron N5010 laptop. Its battery has been dead since years and I have been operating it on charger. I had not used the laptop since last 5-6 months. From last few days, whenever I click on 'power on' button, the laptop boots but there is no display. Not even windows logo comes. It is as blank as it was after opening the lid. The laptop definitely boots as I can hear the normal fan and the heat.

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