What would cause a PC's power supply to break?

I had an old computer that I used infrequently. I left for a week or two for vacation, so I unplugged the power cable from the power supply. When I got back and plugged the cable back in, the power supply began to smoke and did not work ever again. Today, I got another old computer. I was planning on taking the power supply included in the new old computer and putting it in the one that died. Before I did that though, I wanted to be sure that the previous problem was caused by the power supply itself and not the computer. (I do not want the same thing to happen to this new one.)