Yes you can put a iPhone 4 display assembly on a iPhone 4S. I have put a Verizon iPhone 4 screen on a iPhone 4S and it works perfectly. Only modifying was the bracket near the SIM card holder has to be cut off the Verizon iPhone 4 screen because the Verizon iPhone 4 doesn't have a SIM card holder. When putting it on this bracket hits about dead center of the SIM card holder on the iPhone 4S frame, just cut it off and Voilà everything else fits the same. I wouldn't recommend doing this for a customer, only for you or friend in a Pinch.
Are all the small contacts on the speaker enclosure pressed down properly? Did you clean them off? The oils in your hand will cause a grounding issue, clean them with 90% alcohol or electronic cleaner before reinstall. For refer I'm talking about the 4 small legs that you have to press and sometimes pop in place before screwing the enclosure down.