video editing pc help

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Hi guys , my son needs a pc for mainly video editing so he needs something with a bit of grunt and stable . his present pc is falling over when converting and exporting large files . he does not want it for playing games but would like to do the other everyday things with it we have a budget of about £300/400.
the current pc has a amd fx 6100 6core at 3.6ghz the motherboard is a gigabyte fitted with an amd radeon r9 200series and 16 gb ddr3 ram.
when editing the system runs very slow and a warning sound buzes now and again , so any advise would be very welcome.

thanks

 

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thanks for the prompt reply Mickyflinn would I be able to use the ddr 3 and the graphics card with that board ,also with the buzzing under load we cant tell if any of the parts are failing , would it have the grunt for editing ?.