I had this happen with my TF300T. Worked fine for about a month and a half, and then simply would not turn on. (Although in my case the 300 has never made ANY sound when turned on -- no vibrate or anything, unlike my TF201.) Same problem with the charge light on the power switch not showing it was receiving anything. I have a dock, and it was showing the green light but the tablet wasn't. I tried everything -- charge from the dock, charge directly to the tablet, charge via PC, long press power switch (12 secs and 30 secs and more), power + volume, reset button on side -- you name it. Gave up -- got an RMA from ASUS (they insisted on my sending in the charger, even though it successfully charges my TF201).
Long story short -- I didn't send it in. I was going to this weekend. But... fully two WEEKS or more into this coma, I did a "what-the-hell-let-me-try-charging-it-once-more" -- and the red low battery indicator came on. The orange "I'm charging" light came on. Two hours later, I tried turning it on (still charging) -- it was at 55%. Left it overnight, it was 100%. Works on or off the dock.
A mystery. All I can think of is, there is a "coma" state (I believe others have posted this elsewhere), and the battery must be drained for the machine to "recover" itself. Either that or some other equally bizarre turn of events. Running for two days now. Still silent on power up, though.
Advice -- patience, maybe? Although mine is wearing thin. I love the ASUS design, but I had to return one TF201 because of a bad startup sound and my replacement has quirky screen performance.
Good luck!