If the battery is down but not out and the 12V PSU is working there is a very old trick that you can use to bring the battery back.
Disconnect the battery - surprisingly the negative is best for safety - and connect a 12V 21W bulb (or filament headlamp bulb) in series between the black cable and the battery negative. Turn on the mains and if it is going to work the bulb will light up brightly. Leave if for a couple of hours and the bulb will gradually dim until it extinguishes. Switch the mains off, remove the bulb and reconnect the black wire to the battery. Use a meter to check the battery volts: if it is 10V or higher switch on the mains and leave it for several hours. Eventually the meter should read over 13V at which point the battery is probably revived. If the battery is a bit below 10V just put the bulb back in circuit and leave the power on for a few more hours.
It was common practice to revive wet cells in portable valve radios in this way post WW2 and in the '50's before transistors came into being. I've done it a couple of times on some of our caravans and it has never failed yet!
Disconnect the battery - surprisingly the negative is best for safety - and connect a 12V 21W bulb (or filament headlamp bulb) in series between the black cable and the battery negative. Turn on the mains and if it is going to work the bulb will light up brightly. Leave if for a couple of hours and the bulb will gradually dim until it extinguishes. Switch the mains off, remove the bulb and reconnect the black wire to the battery. Use a meter to check the battery volts: if it is 10V or higher switch on the mains and leave it for several hours. Eventually the meter should read over 13V at which point the battery is probably revived. If the battery is a bit below 10V just put the bulb back in circuit and leave the power on for a few more hours.
It was common practice to revive wet cells in portable valve radios in this way post WW2 and in the '50's before transistors came into being. I've done it a couple of times on some of our caravans and it has never failed yet!