my Galaxy Tab 10.1 was bricked second time in one month, this really is a annoying issue, unfortunately samsung doesn't provide warranty in my country, not uptill now. First time I had to give it to the market for repair, the person charged me around $50 for the repair and did that in one week. The symptom were the same, I turned it off and it never came back online.
Second time, i had no choice but to dive into the issue and solve it myself, as it was totally insane to pay this much for every time my tab throws tantrum at me.
This time I discharged it fully, as you told, and tried to check it by plugging it into the system, but every time it appeared as APX device, so out of frustration I just plugged it in to the socket, and voila the battery icon appeard, i let it charge for sometime, pull out the charger and boot it normally by pressing the power button, and guess what it was back online, with all the data and everything. I had a hunch that it would turn on as, the first time, when sent to market, sharing my lattitude with my dad i was appearing at the shop location, meaning it worked there, that stupid opportunist simply wiped it and charged me $50. But now i know how to save that money
PS: I was able to identify the cause of the issue, atleast what happened with me was that i powered off the tab while plugged into socket both of the time, it never came back. Something you might avoid for this problem to occur.