It sounds like a PSU failure to me. Unfortunately, it could be a couple of other things. Troubleshooting it, I would see if I could borrow a friends PSU first and see if that is the issue. If it still doesn't run, it could be a motherboard issue as well. Those are the two most-likely culprits of this failure. But the first (and most obvious) thing to test is the PSU with a loaner if possible.
What brand/watt of PSU are you running and your system CPU/GPU specs?