X201 cannot boot/work on battery

[obarriel]

I am messing with a ill X201 that has the following symptons.

-Cannot boot on battery
-Cannot boot on battery and AC if the battery is conected before than the AC. If the AC is connected before the battery it works fine.
-It charges the battery properly, but if the AC is disconnected it shuts down instantly.
-After leaving disconnected coin cell type battery for some time I manage to boot from battery. However it will only do this once, if I reconnect the AC and try to reboot it will no longer work.

I have tested with two different batteries (both working well in one X200) and the behaviour is the same, so it is not coming from the battery. I have updated the BIOS and still the same.

Any clue?