I received some medical care while in Arizona, and apparently they used a device on me that was purchased from another company that I was responsible for. I moved to another state shortly after.

Yesterday I noticed that I have a mark on my credit report for the debt placed for collection. I called the collection agency, and they refused to give me anything about the debt (although I assume it is for the medical device) because I had exceeded the 30-day limit. They told me the address they had sent it to, which had some digits transposed. In addition, they failed to update to my new address (because I never knew I was conducting business with them, I could not have told them about my new address).
I had received one bill from the original company 6 months after they sent it and send payment, but apparently they had refused it because it had already been sent to collections.

The collection agency says they will never remove the mark from my credit, and will fight any attempt I make to have it appealed. They made the mistake, not me. I paid the bill as soon as I knew it was due. They refuse to send any info about what the debt was for or proof of the incorrect address they sent it to so I can send it with an appeal. What can I do to fix my otherwise perfect credit?

First, never call them on the phone, have them put it in writing. Also all contact with you to be done in writing. They will trick you.