I'm sorry to hear you're having these issues.
It does seem to be restricted to the box, based on your description above. However, something to consider is that digital inputs like HDMI have a handshake issue; analog connections such as RGB (component) do not require a handshake. The fact that both caused the same issue causes me to lean towards something in the box itself and not a connection issue with the television.
That said, both do have some form of HDCP on them, and when copy protection software in the box is notified that there might be an inconsistency or incompatibility with the signal's destination, it may cause the picture to scramble. The green may be an issue of scrambling (regardless of how poor of a job the scramble is).
It may be a simple box reset that you can request be done locally - some boxes have that ability, but if it's just a phone call for a fix, it may be worth it.
When the green picture comes on, does it stick around indefinitely? Or will it self correct at some point? If it does stick around, I'd try to show the tech - or maybe have some digital pictures or video to show the technician when he comes.
So that's my insight, but I'm here all the time. So if you have any updates, keep me posted. But initially, I'm leaning towards the box. And I'm not just saying that because we make the TVs.
This issue started this past Friday, 2/6/09. I purchased the unit in December and just got my satellite upgrade on the last Friday in January (now using a HR21 DVR receiver). My issue sounds similar to some others that I have ready about, but not necessarily on the same model number.
Essentially, at random times while watching the satellite receiver through the TV, the screen goes to this distorted green image with lots of lines and squares all over it. It is not a solid green color, as it looks like it is trying to display images, but in a very distorted manner with different shades of green. The problem is fixed by powering down, and then back up. Once the issue occurs, I can use the remote to switch inputs, but the green screen remains until powering down.
I have not been able to get the issue to occur while using other devices (dvd, receiver, old sat box for over a month prior to new box).
I have been able to get the issue to occur while using both hdmi ports, two different hdmi cords (one a monster cord), and also a component (Red,Blue,Green) input.
My guess is this is what people are referring to as a "handshake" issue with the sat box, as it seems to be only occurring with that device, though it occurs with the different types of ports and not just hdmi. I am concerned with trying to schedule a service call, as I can't make the issue occur on demand, but rather have to wait for it to happen.
Any help would be appreciated.