I have a Toshiba L750-22Z, but when i try to use it with a battery, it can't get past the bootup screen, & just restarts & tries to reboot. It works fine without the battery inserted, but obviously, one of the main advantages of a laptop is that it is portable & can be used without power, only battery.
The battery & its connections don't appear to be damaged.
I've just tried to charge the battery without booting up, & there's an orange light on the front of the laptop, but when i take out the power cable & try to power from just the battery, i get absolutely nothing, suggesting to me that the battery is dead.
How old is this battery ?
You have a power issue,
Either the battery is dead, (but the restart is unusual.(try a new one, if same issue, it is something else))
or the motherboard has an issue on the power circuit.
Do you have a multimeter ?
On the motherboard, the internal main voltage circuit can use either the 19v from the charger, or the voltage from the battery
But not both together,
this for, a regulator opens or closes logic gates called MOSFETS
This same regulator is responsible for charging up the battery from 19v to a lower voltage, using 2 mosfets (one connected to 19v, and the other to ground, alternating very fast, so that the average voltage is what battery needs)
to make it short, if one of these MOSFETS is defect, lets say shorted (gate always open), the regulator won't be able to toggle, and with 2 different voltages at same place, you have a so called short circuit.
and that's why the regulator wil shut down laptop
so you will have to check continuity on 5 MOSFETS usually (2 at entrance of charger, DC side, and 3 at battery side (2 for charge and one for discharge)
to mesure the MOSFET, use ohm position, and check resistance between source and gain (pin one is marked with a dot, pins 1,2,3 are source, 4 is gate, and other side 5 to 8 are drain)
if you have a resistance of 0 ohms (ore near zero) between source and drain, the MOSFET is dead and needs to be replaced.