Sounds like a PSU problem. Few things to do right away, make sure the PSU fan is still spinning and give it a clean, with it off and unplugged, with air pretty thoroughly (might as well do the system too). Also, to rule out some thing small like a cord or whatever, replace the PSU cord with a known working one and plug it directly into a wall outlet if it's not. There is always a chance you have a bad power bar/surge protector/ups.
Just comes down to a process of elimination. Take it from someone who bought a new PSU when they didn't have to, exhaust the stupid stuff. That being said, if you have access to a known working PSU, do try that first. A bad PSU can be damaging depending on how it faulted.