Nikon P520 not connecting to photo transfer?

I plugged the camera in (turned off) to my computer using the USB cord and Nikon Photo Transfer immediately opened up, but was not finding a source.

Then, I tried opening Nikon Photo Transfer first and then plugging in the camera. No dice.

I tried charging the camera for an hour before trying again.

When I plug the camera into the computer the on/off button turns on for a few seconds and then off, and then the charging light starts blinking.

The camera needs to be on.
A better way is to buy a card reader and plug that into an open USB port.

Vinegar Taster is right

Just use or buy a card reader, things are so much easier that way

Page 76 of your manual explains why the camera goes into charging mode instead of photo transfer mode.