Nah. Just because the PSU turns on doesn't mean it works. When most PSUs fail, they always turn on, and will just cut out and your PC will restart when you are doing something. The timing is random, but since it always cuts out at the same time for you it might not be a dead PSU. Does it POST?
Hardware can be dead but still functional. What I mean is, just beacuse it turns on and works for a little while, doesn't mean it is not dead. For example, some broken things onnly cause the computer to BSoD/restart when they are under load. Think of overclocking, just because it boots up with an insane overclock, doesn't mean it is stable. As soon as you put it under load it will just crash.
A CPU dying is actually quite rare, you really would have to hammer it. But nevertheless it does happen. And looking at your rig, the overclock and voltage are nowhere near destroying the CPU. 3.4Ghz on an i7 is low and the voltage is very low too.