Computer shuts down when running scans

My computer has been turning off completely whenever I try to run my Norton
Antivirus or Adaware scans. I am unable to remove the files that these scans
find because it turns off in the middle. I called Dell and they had me
running tests on the harddrive and scanning it but it shut off again. Has
anyone had anything like this happen to their computer? and what was the
source of the problem??

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