high pitch whine from computer on start up and running?

Take the side of the computer case off and listen to where it is coming from. It could be one of a few things.

CPU fan.
Put your finger carefully in the CENTRE of the fan to slow it down or stop it FOR A FEW SECONDS. Does the sound stop?

Graphics Card fan.
Does your graphics card even have a fan? Do the same thing as above. Does the sound stop?

Power Supply Fan.
Is the sound coming from the power supply?

Hard disk.
This would mean that your hard disk was about to fail. Back up all your stuff before replacing the hard disk. If you disconnect the power and data cables from the hard disk whilst it is off and then switch on does the sound still happen?

For the CPU and Graphics card fans you can clean them with compressed air in a can or replace them.

Power supply fan: clean with compressed air.
 
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