I had this issue with a Dell Optiplex GX620. It turns out its the capacitors that are bad. The caps are failing so the motherboard cannot regulate where power goes or should go. This results in pressing the power button multiple times to get pc through the post menu… or long beeps and nothing or finally black screen of death… Below is a video on how to do the repair and a link to the guys I got my capacitor kit from.
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