I put new batteries into my nikon camer after I was alerted with the ''battery exhausted'' screen. It now won't turn on.

Get your camera checked for short circuits et al.

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Remove the battery imediately, the memory card and the lens. Place the camera body, lens and memory card in a warm dry and place for several days to dry out completely.
When the camers is dry, insert the battery, lens and memory card, turn on the camers and set the date and time.
If the camers does not work charge the battery and try again.
If it still does not work then you need to send it to the Nikon service centre for repair.

Remove the battery imediately, the memory card and the lens. Place the camera body, lens and memory card in a warm dry and place for several days to dry out completely.
When the camers is dry, insert the battery, lens and memory card, turn on the camers and set the date and time.
If the camers does not work charge the battery and try again.
If it still does not work then you need to send it to the Nikon service centre for repair.

See my tips low power warning full charged camera batteries
Your Nikon Coolpix 5600 camera need Alkaline batteries, Nickel manganese batteries, or Li batteries

Use only Nickel -Hydride battery for your camers.Dont use pencil battery that we are using for remotes ,clock etc

short circuits in the mother board,get it to camers tec.

Well, alkaline batteries don't last long in a power-draining camera like the Coolpix. Try some rechargeables and keep spares fully charged.

To reset the camera, remove the batteries and leave them out for approx. 1 hour then replace the batteries. See if the camers works again.

How could I resist assisting someone with the handle 'Charm City'? What I would advise is getting some good quality 2300 mAH or 2500 mAh re-chargeable batteries - although all batteries have a nominal 1.5v output, not all can provide the sustained power necessary for the camera.