Toyota Repair: alternator, toyota corolla wagon, fusible link wires

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vehicle loses all power except lights . new batterys die out.   ground wire acts eratic .starts with jump start ,but soon dies out.   help  s.o.s, my middle name is duane and i'm dwowning.    1981 toyota corolla,wagon.
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You need to have the alternator output checked it sounds like the alternator is not charging the battery.          follow up response,,,,,,, i have changed the alternator twice(via junkyard) first one was apparently no good ,i was still able to jump start due to dead battery....second alernator ,unable to start cause of no ignition at all,,, cannot even jump start .  did i polorize somthing?  sombody said battery has been ruined.
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I just need to know one thing now, does the car start and keep running with a jumper battery connected and does the engine die when you disconnect the jumper battery?    response follow up; fully charged battery ,cannot  start due to no ignition dash lights at all no power from key,cannot jump or push start .cannot test  second junk yard  alternator by way of starting and pulling baterry cable because of no ignition. yes firt alternator was not charging battery and probaly the second is bad to,,, but still no ignition.  

Answer
Check the fusible link wires coming off the positive battery terminal, they are heavy 10gauge wires, they can look ok but be burned out internally, open the insulation and check, thet are about 3 inches in length and then connected to regular wires. These supply voltage to the ignition and headlight systems.