|"120 VAC with reverse polarity "|
Usually that is more likely to cause the computer to misbehave that it will damage it. However, the metal of the power supply and computer case is supposed to be connected to the "neutral" side of the connection, not the "live" side of the connection, so when those connections are backwards, touching the metal on the case in certain circumstances (e.g. your skin is damp or wet and your feet are on a solid surface rather than a rug) can electrocute you, or at least you're likely to feel it.
It's unpredictable whether a PS has damaged something else while failing. It's less likely if the PS is a quality brand, but brand name computers typically have el-cheapo power supplies that are MORE likely than average to damage something else while failing. E.g. if the PS brand is BESTEC, it's a lot more likely to damage something else while failing.
"If you are lucky you may not have damaged anything else but there is the possibility that the motherboard was damaged. The only way you can tell for certain is to plug in another power supply and test it."
"It may well have taken out your motherboard and more besides the PSU."