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Connect your tablet to a wall charger > press and hold power & volume up for 10 seconds > let it charge for 2 or 3 hours
"I'd rather be hated for who I am, than loved for who I am not." Kurt Cobain (1967-1994)
I'm afraid to say that this sounds like your tablet is dead and your only options are to either return your device to the place of purchase or contact Xperia care and have it inspected http://www.sonymobile.com/global-en/support/contac
His tablet isn't dead. MANY people are having the same issue where it won't turn on or start charging. It will randomly start charging and turning whenever the stupid thing feels like it wants to start charging. A TOTALLY ANNOYING DEVICE! I AM LIVID! I used to trust Sony but after spending this amount of money for a product that started doing this 6 months after buying I will never buy Sony again!
I know this a couple years after this problem started
Recently my Xperia Tablet Z did the same thing.
Wasn't used for some time. I tried to power it up - nothing. Tried to charging it. Nothing. At some point red light came on and it didnt do anything doesnt matter if it was charging or not. I heard 3 x blinking red light means batter dead. After i tried every possible combination with buttons I gave up. Next step - taking it appart. Its pretty easy. The back cover comes of after u use small plastic pry tool...and go around the edge. It is glued but easy to peel off. I also used the heat gun (u can use blow dryer) to help a little (but i think that heat gun fixed the whole problem) While doing that heating up the back cover I have noticed that the red light is off. It seemed like the dead battery got little warm and started to work. I pressed the power bottom and now the red light was flashing 3 times (it never did before) So I stopped with taking the tablet apart and connected the charging cable. The red light came back on and my screen turned on showing that it is charging. Problem solved. I know its stupid but I think that battery got so low at some point of not using the tablet ( and the place was cold) that it needed little warming up. Hopefully that helps.