I would suggest removing the transmission dipstick and examining it. If the dipstick is blackened, the trans is toast.
If the dipstick has a burned smell, the trans is toast.
If the engine was operated with no fluid in the trans as you say, the trans is toast.
Considering the radiator problem, more than likely a trans wipeout, and even a potential engine problem, the car may be history. No way is it worth sinking 500 into just for starters.
He's better off doing some footwork and finding another car. It may be an older one, bland and boring, and even downright ugly, but the object is getting from Point A to Point B.
Your friend is partly to blame for this. One does NOT continue to operate any vehicle that is suffering a bad coolant, trans fluid, or engine oil leak. If one chooses to continue on while praying then bad things will probably happen in spite of asking for divine intervention.