My Coco III is also dead. Green box with no text. I
 think the 6809 is bad. At least, that's what I've been
 told about these units. So, I'd have to desolder it
 and put another one in just to diagnose it. 
I have a CoCo 3 service manual here, if you want me to look anything up
(like the schematics...)
Before assuming the 6809 is dead, I'd want to do some tests. Is there any
bus activity,, for example. Is the RAM being accessed/refreshed? Is the
ROM ever being enabled? And so on...
-tony