How to I switch over to battery when there is no power

With a good fuse and battery, the B terminal of the start switch must be 12V (battery voltage) else bad wiring. I assume the mower starts/runs so this is FYI.

With power at the start switch B terminal, place the start switch in the run position, there should be 12V at the A (accessory) terminal of the start switch. If not, bad switch.

Next, the PTO switch B terminal gets power from the start switch A terminal. If power at start switch A terminal and no power at the PTO B terminal then there's a wiring issue between the PTO switch and the start switch terminal A.

Comment with results and I'll assist further if need be.

Check the fuse panels. If you are not hearing the "clunk" when you cycle the power switch on and off then it's probably a blown 10A fuse for the battery power solenoids.

If the laptop battery is normal, but can not boot, check the power switch. Laptop power switch using a micro switch.

Check the power switch circuit when the power switch is in addition to checking the performance is good outside, but also check the external circuit components for damage.

If the battery power for laptops. But is not charging properly, or does not use the power adapter, then it should be checked laptop power interface circuit and peripheral components.

Start at the battery. Check for clean, tight connections. Any chance it is discharged? It needs to be at lest 12.6 volts on a voltmeter to be ready to start the car.
Is there power from battery to the ignition switch? Turn key on. Do warning lights and gauges come on? And accessories work? Then there is power to the switch. If nothing, start checking fuses and fusible links that pass power from battery to the switch.
An electrical circuit is a complete electrical path from a power source to an electrical load to ground, and back to the power source-the battery. The starting circuit is just such a circuit. From the battery to the key switch to a relay or switch (neutral safety switch) or two, to the starter, and then to ground-back to the battery. If the key turns power on, one could next see if power is getting to the starter solenoid, mounted on the starter. The small wire to the solenoid should have power to it when the key is held in crank position. Use a test light or voltmeter to check for power there. If has power, likely the starter or solenoid is bad. You then need to take it off and have it tested-a free service at most parts stores. If no power is getting to the solenoid, but the ignition switch has power, further testing of the start circuit will have to be done -the clutch switch (or neutral/park switch if automatic trans.), the starter relay, and whatever else is in your starting circuit.
If car has an alarm system, make sure it is not activated, so the immobilizer function is not causing a no start.
Good luck. Post back with results.

You will have to check for power at the switch, and at the motor. Pull the panel off and check the wiring for breaks, first. Then use a battery source and jumper wires to the motor,. to see if it is good or not. You set a battery by the door, and use jumper wires to hook up the motor, one on each side of the battery and the motor. If nothing, switch the wires on the battery-motor should run the other way, then. If nothing still, the motor is probably needing replacement. If the motor is good, and you have power to the switch, the switch must be bad. If no power to the switch, you must have a break in the power feed from the master switch on the driver's door.
Good luck.

UPS come in two types, lower powered cheaper types are usually switch over power.
These units senses a power outage and then switch over to the battery power to generate mains supply. The switch over occurs in milli-secs and does not affect the computer.
True UPS types constantly run off battery power to generate mains supply so there is no switch over time lag. These units are higher powered and higher costs units.

Both type of UPS have the same components.
Battery charger.
Batteries
Inverter that converts battery voltage to mains voltage
Electronic controls

Batteries in the UPS typically last 3 to 5 years and it depends upon several factors. including the number of times the unit must go on battery power and environmental conditions. There are usually several batteries in the UPS and while the battery voltage may show 13 volts, this may only be a float charge/voltage and a true indication of the battery voltage and condition requires the batteries to be tested under a load. There maybe one battery in a set of batteries that is faulty and causes the whole battery system to fail and indicate a battery fault.

These lower powered and cheaper KVA type UPS are switch over types, when the mains supply fail, the UPS switches over to the inverter in milli-seconds which then supplies mains power but the power waveform is a pseudo sine wave (ie not a true sinewave. A faulty inverter circuit won’t deliver power when the mains supply fails.

The true UPS types are usually the higher KVA units (over 1500 VA) that supplies uninterrupted mains power. The mains power is connected to a charger which charges the batteries and the inverter draws power from these batteries and converts it to true sine wave mains power therefore there is no switch over time lag from the mains to the battery.

if you turn off the switch for the interior lights,an override,it will prevent the battery from going dead until you can get the door alignment or switch repaired.the interior lights,there is more than 5 will kill the battery for sure.