I just completed the Forsworn Conspiracy quest and, when I arrived at the temple of Talos, the Markath guards were hostile and said I had to spend the remainder of my days in prison for the murders in Markath. Looking at the quest log, it said I had been framed and would have to speak to this guy in the prison to free my name. But, whenever I try to get the Markath guards to arrest me, they simply go to arrest me then the only chat dialogue is "What's the problem?" (or something like that) and they repeat themselves. What can I do to fix this?

go to jail?

EDIT: I think i read it wrong, try reloading a pre talos shrine encounter save

Same thing here, I've gotten used to entering the city, running to a dark corner and slaughtering all the guards until I can go about my business.

Reload to before you went in and see if that works. The same thing happened to me. Then see if it plays through normally. Approach him, go through the dialog slowly. From what I have experienced, a lot of quest related bugs are from zipping through dialog, rushing ahead of where you are supposed to go, and backtracking and going through the same area repeatedly.

I click "I submit. Take me to jail." and a few seconds later "What's the problem?" comes up as the only dialogue option. I select that and then they just repeat themselves about my crimes. This bug means I can't trigger the next part of this quest line and I am constantly wanted in Markath now.