Make sure the power cable is firmly connected, if it is not securely connected the system will not power on, or it may even randomly power down during use, new power supplies may require a bit of force to seat the power cable correctly.
Check the power button at the rear of the system is in the ON position, most systems have a primary power button on the front, and rocker switch on the power supply itself.
Check for common issues as well, such as:
- Faulty extension leads or multi plugs, try plugging the system directly into a wall socket
- Check the fuse in the cable or try an alternative cable
- Make sure the Wall Socket is powered on, try plugging in a known working electrical appliance.
If none of the steps above solved the issue, the following video may be of help, your systems power switch is connected to the motherboard, when the circuit is completed the motherboard and all other components power on, the connection may have vibrated loose during shipping.