When I created a new character, as I was very bored, which was a Nord, during the quest "No One Escapes Cidhna Mine" I decided to kill Madanach, and be on Thonar's side. After that, when I finish the quest, I went to another hold to become a Thane, and I couldn't become one. I know that I completed all of the favors, but It won't work. Is this a bug?

you killed Madanchs cousin

you shouldnt have done that

Which hold? There is some potentially glitchy stuff in a couple of the Thane quests that AFAIK has nothing to do with Cidhna Mine.

All of them..

Have you done all the "befriend the Jarl" stuff and other prerequisite quests in each hold as well?

Yes.

Well that's odd.

I will tell you I've had troubles with becoming Thane of Haafingar by not following up on the first opportunity to get the quest, which comes in the dialogue with Elisif when you return to tell her you placed Torygg's horn at the shrine for her. The "is there anything else you need, my Jarl?" option comes up then and I've found that if I don't take it RIGHT THEN it will never appear again. Even if all I do is walk over to Falk and buy the house and go back to the Jarl, the dialogue that prompts the giving of the Thane quest for Solitude will be gone. The only solution I've found is to reload to a point before I return to Elisif to complete the Elisif's Tribute quest.

I had the same sort of problem once when I bought Vlindrel Hall in Markarth after Thongvor had been made Jarl, he offered me the chance to buy property in the city and I bought the house and went to look at it before asking him if there was anything else he needed. When I returned to him I could not get the dialogue option necessary to start the Thane quest conversation.

According to UESP, if you complete the Forsworn Conspiracy and Cidhna Mine quests before buying the house, you may not be offered the chance to buy it because you can't get the prerequisite favor quest from the Jarl (I think there are two in Igmund's case, at least there were for me) - which would make it impossible for you to become Thane there. That's the only thing I can find where doing those quests interferes with the Thane requirements in Markarth. I think that would only apply to Igmund because if you've gotten him replaced with Thongvor then Thongvor should offer you the house and the Thaneship as a reward without any additional work on your part.

In Riften, there was a glitch where if you bought Honeyside and then went in the house before being made Thane, the Jarl there would never give you the title when you went back to her later.

In Whiterun you should've been made Thane already when you killed the first dragon in the Main Quest. There are no other requirements. Unless Vignar has replaced Balgruuf and you're trying to be made Thane again, in which case he should offer you the chance to buy the house (even if you've already bought it) and then the "is there anything else you need" dialogue should come up immediately.

As noted above the main problem I've encountered in becoming Thane is from the dialogue option that prompts the quest disappearing when I didn't take it the first time it showed up. Or from the thing in Riften where I went in the house first instead of talking to the Jarl again immediately.

Haven't completed Dragon Rising on my new character.

Lol I thought you said you completed all the prerequisite quests?

You can't become Thane of Whiterun until you've completed Dragon Rising. When you return from completing it, Balgruuf will make you Thane immediately, there are no other requirements but that one must be met otherwise you will not be made Thane.

If you haven't completed Dragon Rising, then you also can't have advanced the CW questline past Message to Whiterun, which means you can't become Thane of Eastmarch because that requires you to advance the CW even further (if you play Stormcloak) or finish it completely (if you play Imperial). You must also buy Hjerim first, which is likewise not possible unless you do the CW questline.

I'm not sure what you meant when you said you'd done all the necessary favors, if you mean the three or five favors you must do for citizens of the hold, that will not be enough. Every Jarl has something you must do for him/her personally before they will offer you the opportunity to become Thane.