In Markarth, I picked up the quest "Speak to Degaine", but he won't speak to me about it, even though the quest indicator is on him.

I previously accepted a quest from him, to steal the statue of Diabella. I can talk to him about that, or give him a coin, but that's all.

Before I report this as a bug - will it resolve if I steal the statue first?

(That's one of several apparently "evil" quests that my PC is avoiding).

I see no reason that it should do so but there have been numerous miscellaneous objectives that different people are having problems with at different times, one of the most notorious being "Speak to the Jarl of Riften" when trying to become the Thane of Riften... It seems that we will all have to wait for 1.4 to find out if they are getting fixed yet...