I replaced the IC with a new one, and now it works correctly. It still whines for a second or so, but I believe that this is normal.

But, now I discovered that the display flat cable is broken, as I can't adjust the contrast (it goes only up, but not down).

Is there a way to repair the cable? There are only 2-3 vias that are broken.

I also found out that a SMD wirewound resistor .1 ohm WSC-1 is open. It is connected to the battery and it seems it was used as a fuse. This probably explains why the battery wasn't charging.

Can I replace this resistor with a jumper wire?