I will add more to this tomorrow (it's late here now), but in case anyone needs it:
We just upgraded to AGS 10.3 in all three environments. Dev and Test were fine, production was fine, but we could no longer log into AGS with the admin account. After a ton of fretting, we discovered it was due to the admin account's password beginning with the "<" symbol.
I will provide a full workaround in the morning, along with calling Esri.
Due to an oversight when ArcGIS Server was initially deployed in our Department, there remained only a single administrative account in ArcGIS Server--the initial one used for the AGS install. When we upgraded AGS to version 10.3, we could not register the Web Adaptor with the ArcGIS Server account, and we could not log in to AGS. As this was the only Administrative user, this posed a significant problem.
As it turns out, the password requirements must have changed between 10.2.2 and 10.3 to no longer permit a special character as the first digit of a stored user's password. I have not performed the testing to determine if it is only the first digit, or any additional details. I have not yet found any documentation to reflect this.
There are two ways to get around this. We replaced the super.json on the inaccessible server with a copy of super.json from the accessible test server. This allowed us to log in using the test server credentials. And then I created an Administrative role, added appropriate personnel, then confirmed the password issue.
The other way to potentially fix this is the link noted below, which I didn't see before finding the alternative.
So, long story short: if you are soon to upgrade to ArcGIS Server 10.3, make sure you do not have a special character in a password's first digit.