The only realistic fix option for this is to check that the camera's battery contacts are clean and bright. If not, then clean them.
Otherwise, the most common cause of the fault which you describe is a faulty power switch. Sadly there's no longer a fix for this as it requires a replacement switch assembly and they're no longer officially available. The 3200 has been out of production for over five years now and is no longer supported by Nikon. Expect the switch to cost more than the camera is worth: you can get perfectly good working examples of the 3200 or very similar 3100 for less than the cost of the spare part or even for free on FreeCycle/Freegle.
You may find a switch for sale as an NOS item (New, Old Stock) but the fault was such a common occurrence that most will have been used to repair faulty cameras. If you get lucky then you'll need to remove the camera casing to replace the switch, I haven't done this on the 3200 since around 2006 so can't give you any specific guidance, but I do recall that it was a *very* awkward job. As with all simiolar products you'll also need to be very careful not to unnecessarily disturb any of the flexible circuit board connectors inside the camera and to take anti-static precautions such as wearing an earthed wrist strap.
Getting a professional repair is completely out of the question as labour charges will cost far more than the camera is worth. Most professionals would also advise that repairs are at YOUR risk; there's a high likelihood that during any repair attempt another, irreplaceable, part may fail.
There is also a chance that the fault may be caused by another faulty part, but finding out which one will still involve partially dismantling the camera and methodically testing the components. You can buy downloadable repair manuals to help you but you'll be up against the cost/benefit argument again as they'll cost more than the camera is worth and may not result in a successful fix.
One final point to consider: your camera has already exceeded it's five year maximum design lifespan, and few digital cameras get much older than that as the image sensor usually fails. Any repairs you do make are unlikely to result in much of a life extension for the camera.
Manufacturing technology has improved since then and image sensors should now last longer so maybe it's time to let your camera go to
Silicon Heaven...
I hope that you've found my posting to be of some assistance, and hope that it helps you to decide whether to attempt a fix on your camera. All I ask in return is that you return the favour by taking a moment to rate my answer.
