No Crank, Start or electrics

My son has a '94 geo metro, 1 litre, 3 cyl, automatic transaxle, w/ TBI, approx 170,000 miles. Engine is one year old. For about two weeks it has been intermittantly not cranking, and sometimes had a delay to start when it was cranking. Half a second delay or so.
We cleaned the battery and put a new cable end on the positive cable. We also put in a known good starter from his previous geo ( same year and engine). Today, he drove 5 miles up the road to pick his brothers up from school and after sitting for about 15 minutes, it would not crank. He had no dash lights, indicator lights and there was no clicking from the starter. I went through 4 hours of diagnosing and this is what I have found so far. When the battery voltage is measured at the battery, 12.7v. But when I plug in the fuse for the tail lights, it drops to 1.5volts. It took a long time to get to this point as I was not able initially to determine why the battery had 12.7volts, but when I measured it at the main 60A fuse, it was only 1.5volts. That is when I began unplugging fuses to see it there was a circuit that was drwing the voltage down. The Tail light fuse is the only fuse that has an affect on the battery. Even though the battery voltage would come up to 12.7 v with the tail liht fuse out, there still were no dash indicator lights and the engine will no crank.
the voltage at the solenoid wire is also low. We had to take a break so I took his battery down to a parts store to have it tested. There machine indicated that the battery was bad and it recomended to replace the battery. It never even gave it a charge. I sure do miss the older machines with the carbon pack and the dial guages for voltage and amperage so I can actually see what is happening with the battery. So, I bought the new battery and drove back up to put it into the care. The headlights actually came on for the first time since the car quit cranking. So, I gave the key a twist to see if it would crank and it immediatley lost all electrical power and the lights went out. Never to come on again. I never recall seeing any dash warning lights come on when I went to crank it with the new battery. The voltage again dropped down to 1.5-2 volts at the 60A fuse. It almost seems like a bad ground, perhaps at the transaxle. You know how sometimes when the battery connection is really bad and pops and smoke due to that poor connection? Well, that is kinda what it seems like. Any suggestions?