Final Analysis

Based on your input:

My Computer is completely non-responsive when clicking the power button

Conclusion:

This indicates hardware failure.  This assumes that no cords are frayed or disconnected, and assumes your electrical source is functioning.

Quote for Parts, Labor, Taxes, Fees (all inclusive)

Desktop Computer  between $210 - $285

depending on degree of damage.

Laptop Computer  non-applicable  (we do not repair this on a laptop, we recommend trying an alternate power cord.)