No, you can't tell if the regulator is blown/failed just by looking at it. It fails electrically. If you do a search on W140 blower regulators I'm sure you'll find a number of posts on how to test it. You'll also find a number of posts on how easy it is to get to.
If you disconnect the regulator leads to the motor and jumper power directly to the motor, and the motor runs, its almost certainly the regulator.
Don't know where you went looking for parts, but 127 dollars is pretty cheap. You sure you got the right part? I'd expect the blower motor (alone) to be over 200. Same for the regulator.
Gilly is absolutely right... change the filter before you put it all back together.

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KenP

1996 S500 W140 Coupe