I know that this is probably useless, but, look at the header on your Quest Watch. Is the green button on? That is the one that controls whether the quests show on Carbonite's map or not. It has to be
BRIGHT GREEN to be activated and showing the quests.
Click the pictures to get a larger view. View might open in a new browser tab or window. Size is 1600 X 900.
On and activated.
Off and deactivated.
You can see the Quest Watch header above the map. Notice the
GREEN button. It is all that I changed.
EDIT: Just for comparison, I decided to post screenshot's of the minimized map too.
On and activated.
Off and deactivated.
The Quest Watch header is at the top of the screen, near the middle. Notice the
GREEN button.
I don't know why it is like this, but, this seems to be the only place you can turn the quests areas on and off on the map in Carbonite.
/EDIT