I was wondering has there ever been a moment where the joker is ever serious?

Well Joker was written more evil than funny in his oldest appearances. In the Joker graphic novel  http://www.comicvine.com/joker-joker/37-141427/. When Joker had his transformation in The Clown at Midnight http://www.comicvine.com/batman-the-clown-at-midnight/37-106607/ and in RIP he was also pretty intense. Same as Dark Knight returns. The Killing Joke as well.

The Joker is dangerous because he can switch from comedian to monster in an instant. He's serious as often as he is comedic. 

Pushback/Payback, when he, in an oh-so out of character way, missed his wife & wanted revenge for her death. Not only was it OOC, but it was unresolved. Hardly forgivable. I wanted to see Joker & Hush duke it out.
 
He's had plenty of serious one-on-ones with Batman & he seems serious when fighting hand-to-hand with anyone who isn't Batman. If you can make him angry & unammused, he's plenty serious...just not often.

There was the time he killed Sarah Essen-Gordon (James Gordon's second wife). Joker had kidnapped all of these infants and Sarah had to choose between herself or the children. She saved a baby Joker dropped and at that moment of opportunity, Joker shot her, leaving her surrounded by the babies and Joker walked away with a frown.

I have seen him plenty serious with Harley. Especially when she pisses him off or when just wants to get away from her.

Sometimes I think Jay is just a tad bit more scary when he isn't laughing.....depending on the situation of course.