Will not turn on
Will not turn on when button is pushed
What is the model number of the desktop?
Try disconnecting everything from the motherboard except the PSU, the RAM and the video card (if not using onboard video), i.e. HDD, ODD, any other cards etc. and see if it starts and if you can get into BIOS.
If the PC still doesn't start, try the paper clip test to see if the PSU starts OK. Here is a link that shows how to do it. If the PSU doesn't start using the test method it is faulty and needs to be replaced.
If the PSU does start OK, then use a DMM's (Digital Multimeter) Voltmeter function to measure the output voltages from the PSU. Also check with the DMM's Ohmmeter function the the desktop's Power button has continuity when operated.
If all the tests prove OK then there is a problem with the motherboard.
Try this first . Unplug the computer then hold the power button down for 60 seconds then release and wait another 30 seconds then hold the power button again for 60 seconds .Now plug in the computer and try to start it . If you have no joy then you need to replace your power supply .
Hope this helps
Mine belonged to my father in law. It’s a Lenovo Think Centre M58 dead in the water. I went through all the diagnostic advice and determined the power supply was out. I hooked another power supply and unit booted up. I tore the PS down and found several swollen electrolytic capacitors on the PS board. After replacing them the system booted right up.