White wire may be internal thermistor of battery,usually 10kohms at around 20 degree Celsius
Just solder 10k resistor to GND
Battery voltage is between 3.7-4.2V or on some newer 3.85-4.35V or little higher to 4.4V
So at 3.7V it may be not enough.
Also during startup,there are spikes of drawn current even high as 2A maybe,that depends on tablet,not sure about that but I see on some phones, by ex 1.6A during power on sequence (no sim inside so no GSM power)
So if you use thin and (or) long wires for power,voltage drop on their resistance will be high enough to make power management to detect low battery and switch off.
Use short and thick wires for power,rise voltage to 4.2V,use multimeter connected to board (not on PSU) to see what voltage drop have on wires,sometime even thick wires can have some high resistance value.
Also connect a high capacity value capacitor on board where battery was connected.Something 2200-4700uF /10V
later edit
It may be possible,but I don't think there is the case,that on white wire top be thermistor but also some one-wire communication.
To check that just charge battery,desolder white wire from board,add 10k resistor on board in place of white wire to GND and check if tablet works fine.