I feel the two greens are just in your case coloured wire to the pins, not to be confused with earth, and you would be correct to just join the two as per diagram,provided none of the other three cores are linked across, your previous shorting to earth may as you say damaged the old ballast i dont know.
Without comparing to a good ballast its unlikely you can obtain the readings to expect to test.
One test you could try is on the lamps
continunity test between pins 1+2 and 3+4 note the readings
Plug lamp in and repeat from the coloured wired ends, this will confirm your lamps are good and also you have the correct pairs.
Just reread your first post and you say it went with a Bang so yes its likely the ballasts gone, with NO power to the unit, looking at the rear corner of the ballast can you see a black blow mark from the vent slot, thats where the Pcb earths to the casing on tridonic units, alternatively the back casing clips off and you will see any damage.
If you can its usually irrepairable