Unlikely to be the issue, but check the monitor is set to accept display via HDMI. The monitor's manual will explain how, and may involve pressing fiddly buttons on the monitor to change the input.
If there's no joy, shut down the PC, unplug it from the mains, unplug the monitor from the mains, unplug the PC from the monitor, and unplug everything else from the PC and the monitor that isn't the keyboard and the mouse. Leave them all 5 minutes, reconnect the PC power, monitor power, HDMI cable, and see if you get a signal.
If no, look through the PC side panel (or take the side panel off assuming that doesn't affect warranty) and see if there is a 2-digit code displayed on an LED display on the motherboard.
Also don't be afraid to phone the place you bought it from or the company who built it's tech support line. If it's a new system, it has a warranty, and you've paid these people for that as well as for the hardware - don't be afraid to use that resource, especially if it takes a while for people to reply on a forum thread