Is my CPU already dead? Help?

My desktop was working fine until one day it suddenly turned off by itself. No signal was detected by my monitor, suddenly became black. When I try to turn it on, it directs me to where I would chose to go with safe mode or just regular boot. ( it work alright after turning off ) It happened a few times for a few... show more My desktop was working fine until one day it suddenly turned off by itself. No signal was detected by my monitor, suddenly became black. When I try to turn it on, it directs me to where I would chose to go with safe mode or just regular boot. ( it work alright after turning off ) It happened a few times for a few days. Then today, it again turned off by itself. I thought that if I let it rest bit it would be ok again. But this time, when I turned it on, I had power for just a second, then it did not turn on. I then smelled something burning. I immediately turned off the avr and removed connections (USB, DSL, etc) leaving just the unit itself. I then noticed that the burning smell came from my CPU. I removed other hardwares. i know that this is a stupid question, but is my CPU the real problem? or is it the PSU (the PSU is knid of new. and my CPU is core2duo 2.7ghz, kind of old model of CPU)
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