I'm not sure if I've understood this correctly (I was being nosey on the forum lol), but if there 'is' a password to the network/router, isn't it a normal thing that you'd have to enter the password for access?
The bit of a tablet cycling around saying Authenticating - Remembered - Authentic....etc., is a different problem, and on most android devices it will just say Wrong Password instantly instead of cycling, , but there are some that keep doing the cycling around. I've found it to be device dependent than actual android versions or software. Even the same tablet with different ROMs flashed seems to alter them.
There is a thing I found that may be to blame though - and it can be because of the type of security used on the router. I had a couple of older tablets (one using android 2.3 and another with android 4.0) and neither would conect using WPA of any kind, they would only connect to the older WEP security method (or no password at all of course).
Both of those tablets are long gone now though so I can't give any extra details on that part, but at the moment I have a NEXTBOOK Next7P12 tablet that also refused to connect to WPA. But today, it was left on my desk trying to connect to WPA by accident (i'd changed my router back to WPA last week after I'd done my testing with it, and the tablet remembered my SSID, password and kept scanning on its own), well after being alone for an hour, I came back to it, and it's connected at 72kbps :-o Its now been downloading files and searching on Youtube without a problem, yet last week it refused completely.
That just makes things even more strange eh ? Also, I've seen messages on forums saying that a tablet has had to be placed within a few feet of a router to connect, and from then on its happy and works fine lol
Whoever invented the phrase Ghosts In The Machine, really did know what they were talking about!
(i just noticed the age of this thread lol, sorry!)