PS: just replaced two cells, it works. Just in case, to prevent the charging PCB to loose the power (some LiIon controllers can lock because of power loss) I did it one by one. First I removed one cell, soldered replacement, then second one. I estimated capacity of new cells using Imax B6 charger - both of them were around 3100mah, not bad for noname $12 battery from ebay.
OMG... guys, you need just unscrew FOUR screws on the bottom (two orange circles on the same level that yellow sticker and two orange-circled screws in the middle of left and right side) and then pop the keyboard up with knife, etc, and disconnect the cable.
Thanks for letting us know that battery PCB takes LiIon cells replacement. I have the same problem with reboot using cheap ebay replacement battery. Going to test new LiIon cells for capacity and if OK - will resolder them.