I discovered, I was indeed looking at the wrong pins. I do have a signal on pin 13 of the '244, and nothing on the output, pin (7) even without the FET in the board.
Both of them do the same thing, so I have to get the part. They're labeled HT244, so I'm wondering exactly what they are. You don't happen to have an actual part number for them, do you?
There is a difference in the two boards. The second board works exactly the same way except when I turn on the smoke, it shuts down the board. However, if I don't turn on the smoke, it's identical operation.
I'm thinking whatever happened to the P/S that has the cooked FET may have damaged the same component on these boards. As George says, it could have been a reversed battery, that FET was really smoked!