The Sun Solaris x86 system seemed to accept my username and password when I do SSH, but then the login prompt went away or hang. What happened?
Do you have any option to check the /etc/password file? Please check what shell is assign to you?
Try to connect to system through FTP instead of SSH. If the connection go well then it means logging shell is not assign to your user id.
Your disk could be full, not allowing /var/utmpx or wtmpx to update.
Tom de
Though its not necessary that it will prevent you from logging in.
which user? root?
user locked? cat /etc/shadow
By default ssh using root is disabled.
Let it sit awhile and see if the prompt eventually appears. A prolonged delay at login time can be caused by a non-responding NFS mount or a poorly configured DNS system.
True, but it's happened to me a few times. 
Try the following: log onto your system as some working user and change to the requested. if this works, logging is i.O - you may need to check the users rights to access $HOME.