I think my Rad. is F--- It turns a white or Yellowish kind of milkshake. I was told that maybe the coils inside broke has anyone else ever experienced this.

Milky muck in the coolant can be motor oil too - and in a Neon thats not as rare as it is with some cars. You might want to do a compression check, to see if there is a headgasket going bad. I think that with Neons the headgasket can begin to between the water jacket and the oil passages in the head - and not affect the headgasket.
If the leak is at the transmission heat exchanger, there would also be some coolant getting into the tranny - and making the ATF sort of sudsy.