Need a bit more info, image 4 is not a model number. Even a photo would help.
A soldered in battery is for backup during power failures, and should not effect normal use.
A suggestion would be to check the board for a reset button which may or may not help. I have found them to do wonders on older Rainbird controllers.
As a very last resort before replacing the unit, I would remove the soldered in battery to see if it brings it back to live.