My NEC Fuzzy Logic 6.5kg Washer keeps coming up with LE in the timer box. It also makes a high pitched noise with it. I suspect it is some sort of error message? The washing machine is not dispensing water and starting a cycle.

99 percent of the time it is a timer problem. It is behind the control knob on your washer. You can either hire a repair man or change it or do it yourself with the aid of a couple friends. Timer can be ordered thru ebay or an appliance parts outlet. Just need the make and model number of washer. Good project for friends some weekend. Can usually see how to change washer timer on youtube. The best Stan

No. The high pitched noise did not originate in the control panel but rather in a part of the machine that was chafing or rubbing against something. And now the mechanism is stuck. Check for that first before messing with a control panel.

1e fault code or LE fault code?

This is due to the fact that the draim pump is still running DRY and so makes the high pitch noise. Check the timer or reset to a low spin dry cycle. If not check the drain circuit power using a multimeter from the program controller unit.IF there is power and the motor makes noise then remove and check if the pump is clogged, clean and reset.
check this link:
Drain pump

The high pitched noise you hear is most likely caused by the CPU cooling fan on your laptop. If you suspect that this high pitched sound is caused by the fan going out, you can spray your laptop with compressed air to get the dust off of the fan.
This solution will make your laptop work at a cooler temperature, and reduce the noise.

If the problem persists, seek a certified laptop repair specialist.

Generally LE is as you said a load error. This can refer to an unbalanced load in the machine. You should try to redistribute the clothes to even the loadThe addition of a P.I error code indicates it is having problems loading the programmed wash instructions.
The fuzzy logic is a form of artificial intelligence that controls the preprogammed operations of the machine and warns of wring usage.

If redistribution of the load does not work unplug the machine from power and leave for a few hours. Then replug and turn on.load with a few items only and set the unit to wash ...

I've had the same experience with my Speed Queen washer. Approached the accredited Speed Queen agents for assistance, when tech support was deployed to diagnose the problem.
In the end, I was told that the "timer" went bust. So the wash cycle seems to work 100%, but when it comes to rinse and spin the contacts on the timer don't make contact, and the motor waits in anticipation for it's next command, and that the high pitch noise heard.

The LE error code means that you have a motor problem.  The high pitched noise means that the motor sensor has failed and needs to be replaced.  You will need to call a qualified LG technician to replace the sensor.

According to the Samsung website: "The high pitched sound you hear is probably coming from the flyback transformer. The flyback transformer converts the relatively low voltage electricity that comes from the outlet in your home to the high voltage electricity needed to drive the cathode ray tube in your TV. It is not unusual for a flyback transformer to buzz softly when it operates. However, if the sound is loud and high pitched, it probably means the transformer is failing. To eliminate the sound, you will have to get your TV serviced."

First locate were the sound is coming from. put your ear very close to the timer and listen for this clicking sound. remember a timer will make a clicking noise which makes the timer go around. Timers can get noisey with age. The sound might be coming from below also .I would run your washing machine until the part fails. They might also have a motor controller in this unit which is seperate to the timer which will make a high pitch clicking noise.