Why won't my secondhand iPad let me activate an Apple ID?
Any device (whether iOS or OS X) has a lifetime limit of THREE (3) new iCloud accounts can be activated using it.
Once the third iCloud accounts has been activated from that device, that device cannot be used any longer to create/activate new iCloud accounts.
Apple allows the primary and the secondary account, after third they do this to you:
There is no way around that restriction.
Apple does this to prevent people from having free unlimited storage.
So unless you can use one of the exiting accounts you are out of luck.
Here is some more reading material for the one complaining that I did not provide sufficient link/references:
Can we have two iCloud accounts on our iPad?
iCloud on Mountain Lion: one account per Mac or one per user?
https://discussions.apple.com/message/20755523
Primary and Secondary account
http://support.apple.com/kb/ts4020
What this basically is telling you is that you have already used 3 Apple ID's on the iPad (must be some pretty shifty owner before you) so you cannot add anymore to it. Its done.
Even wiping it will not solve the problem as Apple must be very tight with their security and with 3 id's being the limit as said before me, for not allowing unlimited storage.
EDIT:
Turns out there is absolutely no fix. Your iPad wont be able to log into another iCloud.
EDIT EDIT:
Sources:
https://discussions.apple.com/message/24539188
https://discussions.apple.com/thread/4005827