Killua, one more thing you might check while waiting for your replacement screen is the pins on the digitizer connector, both the cable and the logic board. I had a similar situation that I couldn't figure out, and finally got out a magnifying glass and looked closely. Turns out I had bent a couple of pins in the motherboard connector in the process of seating the plug. Using a pair of fine tip tweezers I was able to straighten the pins, and viola!, it started working.
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Edit: Also, pay special attention on the note on [link|https://www.ifixit.com/Guide/iPhone+6s+Plus+LCD+and+Digitizer+Replacement/50676|step 21|new_window=true] that @krzeszny mentioned regarding reconnecting the digitizer cable. I was guilty of that on my repair that resulted in the bent pins.
Killua, one more thing you might check while waiting for your replacement screen is the pins on the digitizer connector, both the cable and the logic board. I had a similar situation that I couldn't figure out, and finally got out a magnifying glass and looked closely. Turns out I had bent a couple of pins in the motherboard connector in the process of seating the plug. Using a pair of fine tip tweezers I was able to straighten the pins, and viola!, it started working.