Hi. Yes they most def could damaged the Wifi Antenna as it adhered just the the R/H of the home button. Poor Wifi is very common on iPad 2 after Digi replacements if you don't know what your doing. You can ask them about replacing it but I don't like your chances as you maybe up for another screen. Hope it works out

Hi. Try a reset (home button power button together until you see the Apple logo appear) We havn't encountered this problem in any mini screen replacements but 3 of the last 15 Ipad 2,3,4 worked fine and then clients informed us of no touch. This sorted the problem out eveytime. Strange as Its only been the last few weeks this has happened. Also you have to take into consideration that being a mini screen it may of failed and a replacement maybe the only solution. As for the WIFI you may need to reset network settings etc. See how you go.

Has the Ipad been opened up for repairs? If so was the battery disconnected?