I am sorry to hear about that. My name is***** am a computer expert with 17 years of experience and will help you as good as I can.
You did everything right already. Turn it upside down and just let it dry up. You can also try to use a vacuum cleaner to dry to suck out some of the white wine. But it is not really needed. Just let it dry for about 24 to 48 hours to make sure there is no more fluid within the electric circuits. Then turn it back on and it should be all fine again really.
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Thanks for your patience and best regards,