On a PC, with no changing of options, the blue "Connect to Partner" button disappeared even though the partner ID is correct and "remote control" is clicked on. It is not even greyed out, there is NO "Connect to Partner" button anymore.
If you have Windows you should be able to use the System Restore, to restore to one of the restore points dated before when the problem started.
I would recommend using system restore, to reset your computer to a date before the problem started. I will include a couple links to instructions on how to do this, in case you aren't familiar. The first is an article how to and the second is a video, so one should suit your preference.
https://www.youtube.com/watch?v=oGXbMyFaROw (YouTube video)
This should help, if it doesn't let me know and I'l let you know what the next option is.
Before you restore the computer.. have you tried to reïnstall the client? Make sure that no options are saved upon uninstalling the current client and reïnstall it.
That's a very good suggestion also. If you are going to uninstall and reinstall, it would be better if you use an uninstall utility like IOBIT Uninstaller or the RevoUninstaller. This makes sure all left over items are eliminated, so you can get a clean install without old remnants causing problems.