Have you been pressing shift to run? Also I find the closet in the basement (room to the south) easier to get to in time, so if you have been trying with the closet in John's bed room, maybe try the one in the basement instead. Hope this helped!
I managed to make it to the closet, but it wont let me get into it, basically, I'm making it to the closet and clicking on it or pressing enter but nothing happens