Where are you getting the parts from? It seems unlikely, but you hear lots of stories of people getting two faulty parts in a row when they're buying replacements. I usually suggest giving it one more try with a part from a different seller to see if it will work.
Check out the parts that iFixit sells: https://www.ifixit.com/Store/Parts/Samsung-Galaxy-S4
Make sure to match your cell carrier to the part you're buying. You're looking for the "display assembly," which includes the digitizer.