Screen showing only black and grey blocks / doesn't respond to touch

Replaced iphone battery, but now the screen doesn't respond to touch. When I first turned on after the new battery, the screen looked a little blocky, but that quickly deteriorated into just a grid of grey and black squares, and then finally just a few vertical lines.

I imagine that there is some issue with the connection between the screen and the phone, but am wondering how best to assure that a proper connection is made. The screen had been working just fine before the battery replacement. This is my second time replacing an iphone battery, and I am at a loss as to what I did differently this time.