If you're using HDMI to connect, make sure the TV is on the correct input as the console will 'wait' for a valid signal before powering up fully (on some TV's).
Also, if you have the 6 wires (3 reg., 3 hd) make sure that on the part that goes inside the xbox it is turned on tv (only white red and white plugged in) or hd (with all 6 plugged in)
Also check the colour of the Power Adapter when you have powered up the x360.
Here is a link to troubleshoot the power adapter based on the colour of the light on it:
support.xbox.com/.../connecttopowerlist.aspx
Hope this helps