It's possible you have another quest relating to the Count that you need to finish first. If you have Ulterior Motives from the Mages' Guild, try finishing that off first.
Did Hal-Liurz go all the way down to the Count, or did she just open the door? If not, try to force her to actually go down the passage, either through Command Humanoid spell or another way.
If all else fails, you could always try the console to force the quest to the next stage.
In this case, I'd think you'd want
setstage MS40 80
which should go to the stage after giving the potion to the Count
when the Countess dies. Note: you'll have to wait 24 hours again.
Hope you figure it out
