Firsts things first.
Connect your ipad mini to a computer and see if anything pops up. IF yes, then good that means theres hope!
while plugged in to your computer ( and your computer DOES recognize the ipad ) Look for display on your ipad. look very closesly... If you see something (apple logo ) but really really dim, then theres back-light problem with your ipad. If you dont see any display but your computer still recognizes your ipad when your connected to it, then something might be wrong with your LCD display so try changing an LCD
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IF changing an LCD dosent fix the problem then it could be something wrong with your logic board.
There could be something wrong with the LCD connector on the logic board. or circuit problem on the board.