Xbox Does Not Come On
The Xbox comes with a power supply and a power cord. Make sure all the cords are firmly plugged in. Push on the connectors firmly in power supply and the Xbox console. Use a lamp or other small appliance to make sure the electrical outlet has power or try another electrical outlet. Be sure the console is in a well ventilated area. It may shut off if it overheats. Also, check that the HDTV is plugged in and turned on.
TV Input Selector
Some HDTVs have multiple input formats along with HDMI, but some also have two or more HDMI inputs. You must have the HDMI input selected that the Xbox is connected to. Check the numbers on the HDMI input ports and compare them with the display on your HDTV screen using input selector. If the selector is in the right position, try using another HDMI input port. If you have another device with an HDMI output, try connecting it to the HDMI ports to if they work.
Check the HDMI Cable
Remove the cables and check the pins for dirt or corrosion. Each flat connector has 19-pin edge connectors that should be clean and shiny. Check the sockets too. Plug the cables back in if clean. HDMI cables don't have any snaps or locks to ensure they are properly seated. But the connector must be firmly in place. Push on the connector to make sure it's fully seated. If you still have no signal, try replacing the HDMI cable.
Defective Xbox
If its a new Xbox, you'll need to purchase a separate cable to check if it is sending signals on other formats, which is not worth the expense. Return the Xbox. No adjustments are possible when connecting with HDMI. If it has been working with another format and you are trying to connect with HDMI and it doesn't work, and you're sure the TV and cable are OK, your Xbox is defective and you need to return it for repair or replacement.