The laptop will only work on the mains cable - HP Compaq nx6110 PC Laptop

check AC - DC adapter could be faulty
Check surge protection if plugged into a surge protected powerboard
Could have a crook powerboard

is there a dark display when you expose your laptop's monitor to light ? ... if yes check out contrast and brightness buttons ,,, if didn't work the main problem could with the monitor's inverter or the monitor leds ... must be replaced ... if there is no dark display could one of many :
1- check the rams (try another ram to test )
2- check the monitor's cable which connected to the main board
3- check the cpu
4- if nothing of above worked replace the main board ...
give feed back if you can ,,,

May be your Power cable is faulty.

Tip

1- just use another cable and check .
2- Use another power socket, may be earthing will be issue here

keyboard error maybe cussed by :
1. the data cable was loose --> open the keyboard from the laptop and the data cable from the laptop than clean the data cable wait until dry and plug in again use the duck tape to strengthen the cable data connection in the main board.
2. dirty --> open the keyboard from the laptop open all the key (carefully) than use vacuum cleaner to clean all of the dirt or use blow it with air compressor
3. moist --> open the keyboard from the laptop than dry it on the sun or yo can use hair dryer

Most laptop can be used in any country.
Check the laptop's power adapter mains input voltage, it is on a label on the bottom of the adapter.
If the input voltage is 100 to 240 volts then it will work in Australia, you may need an mains adapter to connect to Australian 3 pin mains power point or purchase the mains cable that fits the Australian 3 pin mains power point.

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As the fan is not moving,computer is running hot so it is shutting down.Need to check the fan cable, reset the cable,if it works it is fine,other wise need to replace the fan.

Disassembling the Lower Case Assembly

• Disconnect the Bluetooth cable from the main board.

Are you sure that the power adaptor is working? Does it have any light on the adapter box that informs about it's operation?
What usually happens is that the cable going from the adapter to the laptop gets crackled from repetitive bending, either at the plug, or at the box inlet. Inspect if the cable is intact, and if possible, checks if there's a required DC voltage on the plug.
Perhaps you might need a new adapter for your laptop.

pull the battery and re insert it the try your AC cord should cause laptop to do a power search.

Try and change the cable from the router to computer with a new one and do the same with the modem and see if connects. Hopefully it's just the cables that are faulty.

Panic over!! I unplugged the printer from the mains, took out the USB cable etc, rebooted my Laptop, and plugged the printer back in again... this time, when the power button was pressed, everything worked as normal, and it seems to be staying that way.