The green light is stating the unit is active and ready to be used.
A couple of tests you can do to narrow down the potential problem is to:
1) rotate the screen (but do not force it) and see if you get the screen to come on.
2) insert a headphone jack into the headphone port and see if the video output wasn't inadvertantly directed to the composite out.
3) connect to a TV using the HDMI connection. You should be able to see the menu screen on the TV and will be able to scroll through the settings to see if there is a switch set to output to another device (although I don't remember that feature for this unit).
4) Check
www.insigniaproducts.com for a firmware update and see if that doesn't correct your problem.
If none of these tests yield a correction to your situation, the camcorder is faulty and should be returned or used as a science project.
Hope this helps!