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Could be the graphics chip or an LCD panel failure or a simple faulty connection - If it's the two latter then a repair store should be able to fix it and if it's the graphics chip then you will need a repair centre
Hi BFG
Welcome to the community,
You should contact Sony Mobile within your region as well, as you may still be under warranty, using a third party repair agent would void a warranty if you still have one.
Use my signature to find contact details.