I am having a similar issue. I have 2 computers hooked up to Adobe CC, and on one of those, I am getting a message that says:
"Check Creative Cloud Status
Use the Creative Cloud application to sign in, begin a trial, or purchase Dimension.Learn moreabout the requirements.
Dimension will now close."
When I look at the DIY fixes, it is still not allowing me to do anything in Dimension. I am signed in through the CC app on my compter and open the software through My Apps.
I don't know what the first posters issue actually is but your problem is having more than one account or too many devices... It's well known because Adobe cut corners when hocking up Dimension to the cloud app, open Photoshop or one of the older apps, log out of account then back in... If that doesn't clear it then you need to remove some old system from your cloud account to free up space for this computer