DMS,
I was talking with my local JD mechanic about broken front gears on the JD770/790. He said that he has seen several over the years. In his experience, the most common scenerio was running the tractor in MFWD and having the front wheels come off the ground for whatever the reason (bump; digging down with loader; etc.) and then making contact with the ground again with the front wheels still spinning. Something had to give - and it was usually the front gears.
Do you have your rear tires filled? If not, you can do it yourself. There are threads on these forums that describe how to do it.
Bruce