After the cleaning, don't worry about the lithium battery just yet. Connect the charger to the circuit board and see if the charging indicator turns on.

Looks like this circuit board still needs work. The light isn't turning on. Check that the current is 6 mA. The PMIC is often the problem, as it is one of the more fragile components of the board.

Remove any damaged components, find their identical replacements and replace them on the board. Only attempt this step if you have experience with microsoldering. If not, you can consult my recommendations at the end of the disassembly.