Right at the start of the Bleak Falls Barrow quest, when Jarl Balgruuf walks over to talk to Farengar, the Jarl has bugged on me. I talked to him while he was on his way to Farengar, and now he's just standing on the opposite side of the table from the court wizard and refuses to initiate the conversation that will allow me to continue the quest. Both NPCs are still usable, and Farengar will still sell me items. Farengar can also be asked about his 'project' and will tell me to go to the Jarl, while the Jarl has no dialogue options on the subject. I also tried sprinting into both NPCs to try to reset them, but to no avail. I've lost the autosave and cannot go back now to before the NPCs bugged. Any ideas?

It's a longshot, but I have two ideas that fixed two different issues with dialog for me, among other oddities.

First, try saving, returning to dashboard (or exiting and restarting on PC) and restarting, then see what happens. If not, try leaving the cell, save, reload, reenter.

Other than that, I got nothing. Sorry, mate.

Just got this exact same bug, anyone managed to sort it out? (Tried saving/reloading etc. )

Well if you are only on that quest starting over isnt that bad of a deal but if you put off the main campaign and started with other stuff first try waiting 24 hours and if that doesnt work try going through bleak falls barrow and grab the stone and then go back and talk to the mage guy..hopefully that works.

Just go to Bleak Falls Barrow and you won't need to talk to him before hand

Just go to bleak falls barrow, make sure you get the dragon stone, and report back to Fal... whatever his name is, and it should trigger the quest as being done.

Sorry , should have said I already have the dragon stone. Tried sprinting into them, attacking, nothing will sort it.