Camera for Nail Art Photography?

So this may sound strange, but I would like to know what type of camera+accessories to buy for taking nail pictures. I currently have a Nikon Coolpix P510 and really need a new one. My Instagram is youvegot_nail. If you look at my photos you can see that the lighting is weird (not my lights though, it's the camera) and the photos are fuzzy and dull. So what should I buy? Please include specifics so I can buy exactly what I need. Keep price below $1,500 unless truly worth going over. Thank you!

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My Nikon Coolpix p100 camera won't work?

It shows that it's turned on (the green light appears) but the screen is black, and I can't turn it off either. I tried to charge it, remove and put the batteries/memory card back but nothing happens

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