I have a power supply of an LCD monitor. The model is PI-170DTLA and I want turn on the backlight lights without using the motherboard. How do this? What is the pin? What voltage i need? How control the brightness?

How control the brightness? This trouble maybe power supply or inverter boards is defective.
first you can test the voltage of the multr,and then check which part is defective.From Wisiny.com can find those parts
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you can also check this boards whether suit you:
PI 170DTLA 200 000 170DTLAH Proview 860 AB0 170DTLAH Power Supply...

You'll have to power the HV converter board of backlight from an independent power supply with the same voltage and corrent capacity than the motherboard provides, you can use a multitester to get these values or maybe thre's a sticker on motherboard providing this data, use the connector from motherboard to HV converter board to get the pinout, the brightness control can be get varying the provided HV to backlight. If you can get service manual or the circuit schematic of monitor will be helpful for your purposes.