Touch screen unresponsive after screen replacement

The fact that you bought a cheap screen certainly raises red flags. However, the iPhone 6 Plus is prone to developing Touch Disease. One of the common symptoms of Touch Disease is a grey bar at the top of the screen but not every phone develops that. You can access an article I wrote on this by going to my profile for the link. There is also lot's of info on the web.

Do you still have your original, cracked screen? If you do, then I would recommend you try re-installing it to see if the issue goes away. That would confirm that your replacement screen is bad. Otherwise, you only option is to try a new replacement screen, this time of better quality. You can get a good quality screen here and the replacement guide here.

Touch Disease requires a micro-soldering repair and is not a DIY fix.