The only thing that I can suggest is to get a copy of the schematics (supplier example only - I couldn’t find a free download online) and use it to find out why the keyboard backlights are on and why the charging light is not turning on when the charger is connected. That would be for starters. After that finding out why it won’t turn on would be next.
The “no signs of life” without the charger connected most probably is due to the battery being depleted because it isn’t being charged as shown by the fact that there is no charging light when the charger is connected.
It’s down to board level fault finding and having the schematics is a must, for me anyway. I could understand it more if it were just that it isn’t charging or turning on but the keyboard backlights turning on when the charger is connected is very strange."