[Q] Portion of touchscreen not working ( + cost of repair?)

Hello,

My phone was knocked out of my hand by a friend accidentally, and sadly a hairline crack has appeared on the front glass panel.
Now, a portion of the display (perhaps 15% of it) simply doesn't respond to touch at all. Why is this the case when the entirely smashed glass of my old Moto G can still register touch? Is there anything I can do to fix it, and if not, how much would a repair cost if I send it directly to Sony?

PSA: How to get rid of some portion of lag on your Moto X Play

I have found that a large part of the lag most users are experiencing is actually coming from the Google launcher (My launcher is updated with the vertical scrolling app page). Switch to a launcher such as Nova and the you will be able to notice the difference immediately.
I was initially very unhappy with the lags i found while using the phone when i first got it last week but since switching to Nova i've been extremely satisfied with the performance of the phone. Let me know if you'll find a difference too :)