The challenge is that serial transmits 1 character a time. Not the actual key press events. So what the arduino would end up seeing is: "WWWWWWWWWWWWWWWWWWWWWWWWWWW". You'd have to create a timeout for when the character stopped coming in. That's likely to be error prone.
Alternatively, you could have the PC send one character when the key was pressed ('W') and another when the key was released ('w'). The Arduino would then start something happening (set a pin HIGH) when one character arrived and stop it when another character arrived.
Of course, this all depends on what is sending the serial data. The Serial Monitor does not send anything when you press a key. It only sends something when you click the send button. So, there is no possibility of sending different data when a key is pressed and when it is released.
Your own application, on the other hand, could.