I'm going to assume you purposely chopped the first field (user name) off each of those lines for security reasons. If not, that's your problem!
The password you are showing in /etc/shadow is not an MD5 encryption string. Perhaps you hand-mangled it, also for security reasons... I sure wouldn't post my real password hash on a message board (I'd create a valid one, though, with a password I then would never use).
Red Hat is usually set up to use MD5 encryption and shadow passwords. These are good choices incidentally.
Make a terminal window, become root with the command su -, and execute the command "passwd user" where user is the userid giving you trouble. You'll need to type the password twice, as usual, but since you will be root you won't have to type in the previous password. This will fix any problems with the encryption or with the expiration flag fields in /etc/shadow.
If that doesn't work, post again, and we'll see if we can chase down some log messages in /var/log/secure or in the xwindows log file (harder to find).