They will not refuse to work on it if you have replaced the screen. In the past they have voided the warranty for this but now I believe that is no longer the case. Contact them and tell them the situation and I am sure they will tell you how much it will cost for them to do the repair.
There is a small screw on the back side of the button that holds it in place - it sounds like the screw is starting to come loose. You will need to open the phone up and tighten that screw on the back of the button - only tighten until it is snug, do not over tighten.
I had the same problem after I replaced an iPhone 6 battery. What had happened was the the ribbon cable to the speaker had a small tear in it - I believe from the screen opening up too far when I replaced the battery. Since you have just been in there working on the battery I would open it back up and check that cable.
Try this: Restart your phone Go to Settings>General Management and select Reset Select Reset Network Settings Test the network connection If you still cannot connect to the Network go to Settings>Connections>Mobile Networks Select Nework Mode and switch to WCDMA/GSM Then select Network Operators and tap Search Networks When the search is complete, select your Carrier and test the network connection