WHAT SHOULD I DO NEXT TO IDENTIFING THE PROBLEM?

Do have a 700r4 transmission?Did it start out by you loosing fourth gear then shortly after all the gears?So you have 0psi line pressure in the transmission?

IT HAS A 4 SPEED AUTOMATIC TRANMISSION #4L60-E.
ALL THE GEARS WORKED, THERE WAS NO SLIPING, OR ANY GRINDING NOISES. EVERYTHING SEEMED TO BE WORKING FINE. THEN I CAME TO A STOP AT A RED LIGHT. WHEN THE LIGHT TURNED, IT WAS LIKE THE DRIVE LINE JUST VANISHED - IT SIMPLY WOULD NOT MOVE. IT WOULD NOT GO FORWARD IN ANY GEAR OR GO INTO REVERSE. I HAD TO HAVE IT TOWED HOME. THE TRANS FLUID LOOKED OLD AND BROKEN DOWN OR DELUTED, BUT THERE WAS NO NOTICABLE SHAVINGS OR DEBRIS IN IT. I REPLACED THE FLUID AND CHANGED THE FILTER, BUT THE PUMP DOESN'T SEEM TO BE FUNCTIONING. A COUPLE OF MONTHS EARLIER, THE HEATER CORE WENT OUT & MY BOYFRIEND PUT SOME KIND OF ADDITIVE IN TO FIX THAT PROBLEM (HE DOESN'T REMEMBER WHAT IT WAS CALLED) - COULD THIS HAVE CAUSED THE PROBLEM I AM CURRENTLY HAVING WITH THE TRANSMISSION?

The stuff for the heater core went into the coolant not the transmission fluid.The stuff put into the coolant will eventually clog the heater core etc.Thats what those stop leaks end up doing.Again how do you know the transmission pump is not working?Did you hook up a transmission pressure tester and do a pressure test?

NO PRESSURE TEST WAS DONE. HOWEVER, WE CHECKED THE TRANSMISSION FLUID LEVEL BEFORE AND AFTER STARTING THE ENGINE. THERE WAS NO CHANGE IN THE LEVEL - THE FLUID DID NOT GO DOWN WHEN THE ENGINE WAS RUNNING.

Alright the first thing we need to do is a pressure test not a how far the level went down when it was started.