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I take it the CPU fan is spinning but nothing is turning-on. When it comes down to it - it could be, in typical order: 1. PSU, 2. MOBO, 3. RAM, 4. GPU...
Need more information:
MOBO {motherboard}
CPU
GPU {graphics card}
PSU {company, Watts, and model}
RAM
Also, was there any odd behavior leading up to this problem? Example - suddenly turned-off, lines on the screen, noises, smells, etc.