You're probably dealing with just a cracked screen, assuming the holes weren't caused by a severe puncture and just by a drop or something. Plug a USB cable into a computer, see if the computer recognizes it. If it does, problem solved: replace the LCD/Digi assembly and you're home free. If it doesn't, you may have a damaged logic board and should explore that along with alternative problems (bad charging cable, bad battery, bad charging port, etc.)