Aksher
The messages that you post are not particularly informative and do not seem to be related directly to the success or failure to login.
I would interpret the first two messages to indicate that two TACACS servers had been deleted from the config but that there is still a TACACS server group configuration that references these servers. And the third message is quite clear that someone had telnetted to the device and has made configuration changes (including the removal of the TACACS server definitions).
If there is still a TACACS server group referenced by the aaa authentication commands but the servers referenced in the server group are missing then I can believe that this would cause login via TACACS to fail.
If this does not explain the issue then perhaps you can provide a bit more detail about what is going on?
HTH
Rick
HTH
Rick