Hi,
I have, somewhat, the same problem.
I've tested the battery and it's fine, I took it to a specialist and he told me that the chip responsible is the one controlling the charging process.
Is there a schematic for this keyboard?
He showed me the part but the text printed on it is "home labeled". How can I find the correct part?
He told me it's the first chip above the battery connector on the board. (20+4 pins).
Thanks