I've got the exact same problem with a repair I'm working on right now. Home button works fine, no touch ability. I've done several Mini repairs before with no issues, and of course the device was powered off when I took it apart. I've tried several different digitizers on this unit, all with the same symptoms.
There's a piece of tape that holds the bottom of the LCD to the frame of the mini - you need to be very careful taking the tape off or else you can rip the bottom of the LCDs circuits (I don't know what it's technical term is). I did this on my third repair and blacked out a good portion of the LCD.