Looks like it says LM317 (which makes sense, as it's a voltage regulator) (data sheet)

To check it I think you need to feed proper voltage on the input and then check the output voltage. I'd try to find/borrow an adjustable [lab] power supply with adjustable current limiter to power it. Or to simplify checking, you might want to desolder it and put it into a simpler circuit (like one of the reference ones in the data sheet)

The excessive hotness and dead PSUs probably means there's a short somewhere (excessive current drawn through the regulator) - anything else that got hot?

/Michael