Is it possible a dying Cpu can cause random shutdowns or a motherboard?

I need your lights here guys so i can proceed to a new order of a motherboard or a CPU...My system occurs totally random shutdowns somedays 1 up to 4 or more times, but someday not a single shutdown.Computer shut down even at bios with stock settings...

Greetings there,I just jumped from the Mushkin memory 16Gb 4x4GB 2400Mhz to Corsair CMZ32GX3M4A2400C10 32GB (4X8Gb)I only see 32 Gb throught CPU-Z. Bios and system see only 24Windows 7 Ultimate 64Bit3930K @4GHzRampave IV ExtremeGeforce Gtx 760 Sliim...

Greetings there, Im George from Greece and im an owner of Rampage extreme IVMy System specs are :Rampage IV exreme3930K RipjawsZ F3-17000CL9Q-16GBZH (4Gx4)P.S.U 1500W ThermaltakeGainward 550TiMy problem is that when i use these ram with Xteme memory...