Q:

How do I defeat Morokei the dragon priest? 

I have been doing the College of WinterHold quest line and I came across the dragon priest seen in the title.  However when I got to him I noticed that the ghosts giving him his power to stay in the ghost form weren't doing anything to help that power so I killed them.  The dragon priest stayed in that form and I am still not able to defeat him.  
How am I meant to defeat him? 

A:

According to this article on the UESP, you need to defeat the two Ghost Thralls before you can fight Morokei.  However, as you have said, after defeating them, Morokei will not fight back.  This appears to be a common glitch with Labyrinthian, and could only be solved by using the console on PC to set the quest forward. 
Otherwise, your only other option is to reload an earlier save game, likely before entering Labyrinthian, just to be safe. 

 These Thralls are College of Winterhold mages, sacrificed by the Archmage to keep Morokei imprisoned in his ghostly form.  

Per DCShannon, the console command for PC players is as follows:
prid 00086CF4
kill

