Hi Twanger!
That green screen usually means an error with the Chip RAM or Fat Agnus.
Open the case, and try pressing down on all of the socketed chips, especially the big square one (Fat Agnus, which is associated with the Chip RAM). Don't push too hard, the idea is just to make sure things are well seated and hopefully "reorient" the pins to get a slightly better connection.
If you're confident doing it, removing the chips one at a time and reseating them (cleaning pins as you go) might be required.
Good luck!