why is everything in the electrical system failing?

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We have a '92 Nissan pickup. 2 months ago we replaced the battery, a month later the alternator, Tuesday the starter, and today the battery again and the battery cables. The shop is suggesting that the badly corroded cables were causing everything else to fail. On the way home, I made very brief stop and turned it off. It won't start again. It makes a sound like it is trying to start, but weak. Jumping it did not help. The repair shop said they had started it 10 times to be sure I wouldn't have a problem again. It started with just a brief hesitation when I left the shop and I drove 5 miles before stopping.