GT4016 hit pwr button comes on flashes three
Check the USB ports for damaged contacts. If the supply powers up and then shuts down immediately, you have a critical error.
Damaged USB port contacts can cause this but so can graphics cards etc. Open the machine up and remove all cards and memory sticks and unplug all the drives but LEAVE THE CPU ALONE!!
Now, turn it on. If it boots and starts beeping ( which it will with no memory installed) shut it down and reinstall each item you removed one at a time and turn it on after each single thing. When it stops booting and does whats its doing now then the last thing you plugged back in is the issue.
If it still doesn't power up with everything removed then the issue is in the mainboard.
If this is th case, my advice is to seek professional advice..