In one sentence: I did it, I've repaired it
In my case, draining did not help at all. My problem was seriously corrupted /data. It was completely unusable. I could not format it. Flashing did not help because restart after reboot could not update /data, so in fact reflashing was unsuccessful. So after all different updates/flashes/etc this what I think helped me:
1. I flashed via ODIN - CWM 5.0 (CWM 5.5 was bad for me, adb could not connect it) and used adb shell. CWM for P6810, CWM for P6800
2. I used adb shell and e2fsck -yfDC0 /dev/block/mmcblk0p9 (my tab is P6810, for P6800 mmcblk0p10) for a dozen of times. adb connection from time to time was disconnected. So I had to start over and over, but every time I did small repairs Then it stopped on 60% (inode clone)... because of -y option it tried to recover lost files, but since I have full buckup, I did not care about it. So I used manual mode -fDC0 and I pressed N for the rest of questions about inode. Then I fixed all folders. Finally after 4h of adb session I got (almost) clean e2fsck.
3. I tried format /data from CWM recovery. It went FINALLY smooth!
4. Reflashed stock FW. After reflashing it, reboot went so quickly that even did not realize it happened. And I saw Google's "WELCOME"
I hope it helps someone.
Don't give up if battery draining did not help. Try to flash CWM 5.0 and check all partitions with e2fsck, and be patient
I cant get into recovery, no matter what.
I can get into download and have flashed Stock HC, ICS, different version of CWM. Still cant get into recovery.
Only thing that works is download mode, and flashing via ODIN.
When the tablet boots, it stays on the logo. Anyone know if this can be fixed?
BTW I've also tried draining the battery.