The desktop computer won't turn on; what is the first thing you should do?

check the power extension first. 

1) check the power switch

2) check all the power cables and display monitor

3) check the power supply is working or no

1. Check the power cables connected properly.

2. Make sure the power switch turned on.

3. Check the SMPS whether is working.

check if its plugged in to a power outlet

First Check A.C. Supply or UPS Power. 

check if its plugged properly then observe some cables

Check Power Cable & Switch Mode Power Supply.

Check Power cable and Power Supply