Share your experience!
Hi @NewbieMe, welcome to our forum!
I'm sorry to hear about your phone. 
If you rotate your screen to landscape mode are you able to use these letters in this mode?
If you can't use them in landscape mode either I'd recommend that you try and clear data for the Xperia keyboard application. To do that go to Settings > Apps > Xperia keyboard > Storage > Clear data.
If you can use them in landscape mode, could you please try to run the Touch test in the service menu? To access the service menu open up the phone application and type in *#*#7378423#*#* > Service tests > Touch > Free Drawing test. Are you able to draw on all parts of the screen in this test?
Let me know how it went! 
Thanks for the update!
If you have a screen protector on your display, try removing it and after you have done that run the display test again.
Are you still not able to draw on some parts of the screen? If you aren't could you please try and reboot your phone in safe mode.
When the phone is rebooted in safe mode run the test again or try to use the keyboard. How is it working in safe mode?
If you still can't draw on some parts of the screen in safe mode I'd recommend that you perform a software repair using Xperia Companion. This will delete all data stored on the internal storage, so it's important that you backup using Xperia Companion first of all.
If you need to perform the software repair, try the display out before you restore any backup.
Keep me updated!
Hello again!
To reboot your phone in safe mode, press and hold the ON/OFF button until you see "Power off", "Restart", "Take screenshot" and "Record screen". Press and hold on "Power off" with your finger, after 2-3 seconds you will see a new window where it asks if you want to reboot your phone to safe mode. Press "OK" and the phone will reboot in safe mode.
In safe mode all third party applications won't be started to see if they are the cause of this.
To exit safe mode just restart your device as normal!
Let me know how it went! 
I have the exact same problem with my Xperia Z5 Compact. Initially I found that I could not press the "r" or "x" letters on the keypad when in portrait mode. The keypad skips those letters and types one of the adjacent letters instead ("e", "t", "z", "c"). I downloaded the "Screen Touch Test" app and found that there is a vertical area the whole length of my screen that does not respond properly to touch. I've attached a screenshot (see below), you can see the vertical rectangle, about 1cm wide, that I was unable to color in completely. This happens in Safe Mode as well.
I contacted Sony Xperia Support US. They had me perform a software repair using the Xperia Companion application on my computer. Problem still exists.
I'm still under warranty however I have an international version of the phone and Sony Xperia Support US is unable to help any further (I have to work with Xperia Support China).
I am curious, when did this problem start for you? Mine started around November 29th. I am still hoping its a software issue (so I don't have to send the phone out for repair). However I cannot find any relevant updates that occured at that time.
Sorry to hear that. 
Did you perform the software repair yet? If you haven't done that would be my next recommendation. Remember to do the touch test before you restore any backup!
@KurtMann75, I'm so sorry to hear about your phone. 
Since you have performed the software repair and you still are experiencing this behaviour I'm afraid it sounds like i'ts hardware related rather than software.
I'm afraid I wont be able to assist you getting your device sent to an authorized service centre but I wish you the best of luck when contacting our Chinese support.
Please keep me updated!