You will hear this more than once: never run as root. Use the system as a normal user, and only become the root account temporarily to do system administration.
RedHat normally does not allow root to log into the GUI environment partly because it's a serious risk to the stability of the system. Do not run as root for normal day-to-day use.
During install, there should have been a dialog box asking what users to create. At least one should be created at that step. If the rest of this reply makes no sense, you might consider reinstalling to avoid the confusion and making sure you create a regular, non-root user at this step of the install.
If you don't want to reinstall or can't, then you can log in to a text-based terminal. Hold down this key combination: Ctrl-Alt-F1. That should take you to a text login. The root account should be accessible from here. Use it to create a regular user with the useradd command. Type
man useradd if read how to issue the command. After the user is created, change the user's password with
passwd <new_username>. Then logout of the root account, hit Ctrl-Alt-F7 (which should return you to the GUI - otherwise try F5), and then log into the GUI with the normal user.
If the text-based login does not allow root to connect, then you'll either need to boot into single user mode or use the install disk to enter "rescue" mode. If none of that makes sense, then it would probably just be easiest to reinstall