Won't turn on,even with new battery. Turned on the first time,but 2 weeks later it won't,even charging battery again. Hardly had any use since new, appro 3 years old.

This camera uses a Rechargeable Li-ion Battery EN-EL19 If you let these type of batteries fully discharge then you may not ever get it to take a charge again. You can go for a cheap third party battery and see if that works. It may be the cheapest option. Have a look here
http://www.premier-ink.co.uk/advanced_search_result.php?search_in_description=1&keywords=+EN-EL19&x=32&y=13

More likely to be a battery issue than the camera.

Do the batteries work in another device? They may have just deteriorated with age or being left uncharged.

Are you sure they are rechargeable batteries?

Try replacing them , even with cheap generic batteries if they are AA/AAA just to verify the camera works.

Double check you have them oriented correctly when putting them in.