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Hard to tell, the problem could be due to water damage or it could be because of impact.
That's the water damage in your phone. You're going to have to say rest in peace, OR, get a blow dryer and blow dry into the phone and the heat will evaporate the water, you have to hold it there for 10min or so. Put it back in the rice after you thnk you have evaporated the water. If it still does not work, i would advise you to take apart the phone (if you know what you are doing)
You should take the battery out for this.
Don't listen to @uliwooly
You already voided your warranty by taking the back off.
Your suggestion WILL DAMAGE the phone, that's not ok.
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Thats water damage. Back glass has nothing to do with the touch screen , Only NFC.
First try dong a Software repair with the xperia Companion if it wont work do this :
Since it was in rice and the screen is not working try doing this :
Since your Back is already removed
Turn off your phone.
There will be 5 Flex cables on the phone motherboard 1- Camera (Top left corner) 2- Top microhpone & 3.5MM jack (top right corner)
3- Battery Connector (Its placed right over another connector so they're very close) 4 - under the battery connector i think its to the Magnetic charging port. 5- Screen , Buttons , buttom speacker connector its the widest connector on the motherboard
Unclip the 5th Connector ( The widest) and 3rd Connector ( battery connector) wait a minute , connect them again and turn on your phone.
If it wont work follow all these steps to dissassemble your phone : https://www.youtube.com/watch?v=9ZLLChEXzWk
You dont have to remove the screen. Just clean the connectors with a 100% alcohol cloth and put it back in rice for a few days.