Bad connection to power. If the computer keeps turning on, it could be a bad connection, or a internal problem with the Power Supply Unit such as a loose connection, or pinch wire, or the PSU itself is dying out.
Almost all PSU except for Slim/Low Profile power supplies, have the same practical measurement when it comes to the screw hole aligments with the Case. IF you PSU needs a PCI-E connection, make sure it has two.
To do the installation yourself, I would recommend backing up important folders, getting yourself grounded by touching wood, or getting an Anti-Static Wrist Strap which attaches to the Case.
Open the Case, disconnect the wires to all the Drives, Fans, and the Motherboard. If you need to take the Drives, or Fans out that are in your way. Slide the PSU out and put the new one in, with only one screw holding it to the Case. And plug everything back in.
I would not let Best Buy give you a PSU because they are very cheap, and can easily break down. I would get an Antec or Thermaltake, or Corsair PSU and get Best Buy to install it.
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