Put batteries in and it is still 'dead'

Recorder batteries had long gone dead and one day needed it and swapped out batteries and yet, when I put in a new set, nothing, zilch. No lights, no beeps and nothing on the led screen, but there is - I hope - still a lot of digital files/sound on there that I would like to try to get unloaded/access.

Any place or person that I can go to for repairs/service?