I can't proceed with any quests (the ones I've tried are A Blade In the Dark, Blood on the Ice and Dampened Spirits), because everytime I have to talk to an NPC I don't get the diologue options neccessary to continue, even though the quest marker is clearly over their heads.
I think the first instance was was over a week ago, but I dismissed it, and haven't really played since until today.
Any help would be much appreciated.

You might unfortunately find you have to go back to a save from before that first instance, either that or use the console - (if on PC) - to shift the quests along.