No battery in the thing, still won't start.

Yes, yours as well would run off mains without battery plugged in. Check connectors are well in the sockets and see if there’s any obvious sign of damage on the board, magnification and good light source would help. Quite weird the green led dims at times and is bright green other times. Would be good to make sure you’re using a good working charger by borrowing another one form a friend or check yours works properly on another Mac.

When led is bright green your Mac should start on its own without power button.