Here are some programs I commonly use to test for issues that may help out for troubleshooting upstairs.
Testing HDD's and SSD's:
Testing for faulty RAM:
Windows memory diagnostic in windows (mdsched). Every PC has this. To find out if errors were found after the test finishes, open Event Viewer and on left side expand Windows Logs, select System for the event type, and search for the source of Windows Memory Diagnostic. This will tell you if errors were found on the RAM.
Testing for faulty GPU:
is what I recommend. There is an option to choose to do a GPU stress test, and do error checking. If OCCT detects GPU errors then you can pretty confidently say the GPU is faulty and needs replaced http://www.ocbase.com/index.php/download
*This requires a few extra files that can be automatically downloaded with the setup.
Testing for faulty CPU:
Otherwise, check for issues with drives, RAM, and GPU before saying the issue is CPU related. Note that OCCT can be useful for testing for CPU issues as a general test
If a machine just doesn't turn on, or turns on then off really quick, check a few things first - Do they have cooper heatsinks floating around in their system, coollabs, or ICDiamond? Heatsinks are common to cause issues if they come loose and need to come here first. A shorted machine usually will turn on then off or just not turn on at all.
Also note that Coollabs can come loose from the CPU or GPU if too much liquid was applied and may short out components. All thermal compounds can cause overheating if improperly applied as well - this includes ICDiamond and stock compound. Usually overheating will not cause the machine to post and just sit at a blank screen before turning off... but it's usually rare to get overheating unless the machine is older.