The Fn light being on means that the Fn Lock function is on. The default is that it should be off.
Try pressing Fn + Esc and check if the Fn light goes out and that there is a display by pressing either the F7 key or the Fn + F7 keys
If still no display did you do a full power refresh? You only mentioned removing the CMOS battery.
By this I mean, turn off the laptop, disconnect the charger, remove the main battery, disconnect the CMOS coin cell battery and then press and hold the laptop’s Power on button for 30 seconds to drain any residual power from the laptop and also to reset the BIOS back to default settings in case it was corrupted for some reason.
Whilst the coin cell CMOS battery is out if you have a DMM (digital multimeter) check the voltage of the coin cell battery. If it is <2.6V DC replace it. The battery part # is 04W4118. Search online using the part number to find suppliers
Then reconnect the CMOS battery and reconnect the charger to the laptop. Leave the main battery out at this stage.
Try to turn on the laptop and check if there is a display and that it boots to the OS.
If there is allow it to boot all the way to the Windows desktop, allow the HDD activity to settle a bit and then shutdown the laptop in the normal manner.
Once it has completely shutdown, disconnect the charger and reinsert the main battery, reconnect the charger and turn on the laptop.
If it turns on OK, allow it to boot all the way to the Windows desktop, allow the HDD activity to settle a bit and then check the charge status of the battery. If it is charging allow it to fully charge before disconnecting the charger.