SOLVED... from me anyway.
I have a 2 year old iMac where the logic board had been changed by Apple and no serial number shows up on the system profile (About This Mac.)
I went into System Preferences, iCloud and received the same "Account Limit" message when I tried to set iCloud up.
I called Apple. They told me that iCloud does not check for a serial number.
The tech could not figure out why the account would not work.
She escalated the issue to a higher level. The second tech said I should use another device to create the iCloud account. I told him I didn't have one available (iPhone was in car.) He asked for the account ID and did some checking and said that for some reason the ID (which was NOT a dot me email address) would not convert to iCloud, even though it worked fine with iTunes and AppStore.
He created the account on his end... using my "invalid" ID and a password. Took about 1 minute for the account to be created. I then went into System Preferences and signed in. I also tested to see that I could get in to the iCloud web, and made sure it still worked in iTunes and AppStore.
The tech said this was the first time he had heard about this issue... there was nothing in the Apple tech logs about it (which is why the first tier tech had to escalate it.) I told him to Google for it and he'd see a lot of posts about it.
So if you have this issue, do the "express lane" support process... I got the tech person after about a 1 minute wait (Saturday, 7:30 PM PDT). If the tech does not know what to do maybe they can see case 334530452 assuming the tech made notes on how he fixed it.
BTW, he said that if people call about iCloud issues they don't have to have Apple Care.
Hope this helps.
Al
www.jaya123.com