Machine squeals when filling - Fisher and Paykel GWL11 Top Load Washer

Turn off the water. Remove the inlet hose and clean the gauze strainer, replace and try again. If it still does it, it may be the water inlet valve needs replacing.

This is actually quite common and is a combination of water pressure and the size of the tube in the inlet solenoid, try turning the fill tap down a little and you should notice a change in the squeal noise, in most cases just changing the water supply pressure fixes this but you may also have a failing inlet solenoid that will need replacing at some time in the near future.

most of the time it is the water pump is going bad. It squeals real loud.

The pump needs to be lubed that will stop the squealing, and sounds like the suspension rod need replaced too

The squealing is coming from the impeller seal on the water pump. You can try to lubricate the rubber impeller seal with silicone spray lubricant. If that doesn't work, replace the pump.
It the squealing goes on too long (weeks/months), the seal will begin leaking water onto the pump. Eventually, the pump will rust and short out, possibly ruining the electronic control board -- which can cost big $$.

Is there a faint buzzing or humming noise coming from the water-inlet valve? (The water-inlet valve is the device on the washing machine that the fill hoses are attached to.) If you can't hear anything, the water-inlet valve may not be getting any power. If you can hear some noise and there's water present, you may need to completely replace the water-inlet valve.

Sounds like the pump.  When it first fills the pump recirculates the water, then it comes on at the end of each cycle to drain the water.  The pump is on the bottom of the machine, on the right side. 

Sounds like too high water pressure, could also be dirt in fill valve / faulty valve. Good luck

We took the housing off the washer and started the machine, albeit carefully, and followed the squeal. Sounded like the water pump thingy in the front. Took that off from the machine but still connected to the hoses and the squeal stopped. Dipped and drained machine, removed water pump thingy and looked inside. Found a really beat up hairpin/bobby pin lodged inside! (I have two teen daughters at home) Removed pin, put back together, and wah-lah, a few hundred dollar miracle, no squeal!

Sounds like the gearbox, unfortunatly this is sealed and is cheaper to replace the machine, presume the machine is quite old.