Thanks for all the help in this thread - I finally got my tablet working again ! :-)
Bought my LENOVO TAB 2 A10-70 from Amazon, and was great for 13 months till one day it refused to turn on, completely dead.
1. Open up the tablet - there are no screws, so use a 'pry tool' or 'spudger'. (If you have to, try carefully where the power socket is). After you prise an opening, hold the TAB flat, and slowly run the pry tool around the edge, separating as you go.
2. Disconnect the battery by separating the contact, wait a minute then reconnect. You will need a very small screwdriver, tweezers and a steady hand. Be careful not to bend/damage the ribbon cable.
See this photo which I took from this blog. (No need to remove the battery).
3. Replace tablet cover (for safety).
4. Use original charger/cable to charge for an hour even though it looks like nothing is happening. (Another charger didn't work for me for this, even though my tablet had charged fine with any charger for a year).
5. Whilst still plugged in, press and hold power button for 20 secs.
6. Unplug charger from wall and tablet, and then press and hold power button for 20 secs again.
7. Repeat 4 to 6 until tablet boots (2 repetitions for me, ymmv). (Thanks to Gary, top of page.)
For me, the logo appeared with no boot sound, and then seemed to freeze for longer than usual on the logo, before finally showing the battery-charge indicator at 1%. Took about 5 hours to fully charge (as normal) and seems to be OK now. :-)
This does seem to be a serious design flaw by Lenovo, and I would hesitate before buying this brand again, despite being otherwise very pleased with my $140 TAB2. Maybe there is a specific reason for the TAB to shut down like this when power is exhausted, but to have such a non-consumer friendly fix is unacceptable.
Anyway, good luck everyone. :-)