Maybe I can help you as I just solved my own connection problem after trying to get help from Adobe online support, phone support, and this forum for over a month.
You will need to have access to your Contribute Server installation. If you are using a MS Windows based pc and it was installed using the defaults it should be located here: C:\Program Files\Macromedia\Contribute Publishing Server. Under the CPS folder there will be a number of folders but you only need to open the database folder. Inside that folder will be a folder(s) with it's name being a number [1,2,3 - depending on the number of sites that you connect to]
Inside each of the site folders there will be a groups folder and user folder and a file named connection_key.stc.
I moved all of my site folders to another folder I created off the root folder [C:/contribute database backup].
That has the same effect as deleting the folders, but gives you the option to restore them if you need too.
Then I open the Contribute Client and it allowed me access and I deleted the existing folders and drafts.
Then I went to the site that I wanted to connect to and recreated the connection using the prompts. I had to recreate all of the users and assign their roles for the each site.
I did have a problem recreating one of my sites because it gave me the message that there were "drafts that needed to be deleted or exported", but it wouldn't let me do either of those things. I did a seach of my computer for the word "draft" and it found two files buried in some hidden file. I deleted those files and then I was able to recreate that web site connection.
I think the connection_key.stc file is the important file that needs to be removed as it contains an encrypted string of data.
In fact I also copied the connection_key.stc from one site folder to another and then I was able to get into the site, delete its connection (it was connecting to the wrong site of course) and then recreate the connection.
I hope this helps.
Thanks for your help. I will give it a go and let you know how I get on