New digitizer not responding to touch, motherboard problem?

If the LCD is bleeding or has a black screen or white screen than the LCD has been damaged and needs to be replaced. Replacing just the digitizer will only fix the touch function of the display and not the LCD issues. I would recommend replacing the whole display(digitizer/LCD). This should fix both touch issues and LCD issues. It is also an easier repair with a higher success rate.

As far as the new digitizer you tried, if the ribbon cable was bent to much it may have broken some or all of the tracks in the digitizer cable. This would cause an unresponsive digitizer. Tears in the digitizer cable can also cause this. I wouldn't suspect the logic board unless there has been liquid damage or anything other type of damage that may be visible on the logic board.