Switch pulling 0.44A at ~5V, continuity on capacitor near Audio Codec AALC5638. Fixable?

As title says. I have checked the usualy capacitors and have no shorts, the resistor to the bottom of the audio codec is open load on both sides.


Upon testing the battery I get 2.67 Volts. When I leave it to charge for 2+ hours, nothing happens and there is no sign of life. Is this something that is fixable (i.e. replacing audio codec) or not?

The marked component is a coil. If there is continuity between both sides, I would say the coil is ok.
Under 2.7V the Switch will not power on. I would plug the Switch at a pc usb port and check if the battery is slow charging (it is really slow, if so).