I apologize in advance for making any assumptions, but I ASSUME that you have a J-3 that has SDI output (like a J-30SDI), and are not trying to use a model that does not have SDI outputs on it (you did not specify the exact model, and Sony has many J-3 models, some that do not have SDI outputs).
I would have tried taking the analog composite or analog component outputs of the VTR into the Kona LS, to see if that worked. I ASSUME that the VTR works, and that you have put the output of the VTR composite output on a TV monitor to make sure that it is working.
I assume that you have selected an easy setup with SDI in it, and that you have double checked the Audio/Video settings>Capture Presets, and double clicked on this menu, to make sure that SDI is the selected video input.
Just checking – there are A LOT of menu’s to check .
bob Zelin