Hi,
Here is a video which shows how to replace the screen/digitizer assembly for a Sony Xperia Z3 Compact.
https://www.youtube.com/watch?v=ibb22uof...
Here are some links that show that the digitizer is a separate item and that it can be replaced without replacing the lcd screen, although as the disclaimer at the start of the 3rd link says it is a very difficult process.
The first shows where to get the part. This is not a recommendation either way to use the seller. It is only to show that the digitzer is a separate part and not a part of the screen.
The next two links are parts 1 & 2 of a video on how to replace the digitizer only. Admittedly it is for an Xperia Z3 and not an Xperia Z3 Compact but I would imagine that it would be pretty close to being the same.
http://www.etradesupply.com/sony/tablet/...
https://www.youtube.com/watch?v=levTY6Ix...
https://www.youtube.com/watch?v=BNPeeIAa...
Hopefully this will give you enough information to enable you to resolve your problem.
With regard to not being able to use parts of the screen. As a temporary measure can't you turn your Tablet 90 degrees and use it in 'landscape' mode? Hopefully then the problem area is not covering anything that you need to use.
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The answer guys are volunteers from around the world, You're question was answered by an Aussie!
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