You did not say what version and releast or Redhat you are running. When you install most distros, they will do some sensing of the hardware capabilities. For the monitor, there will be entries made in a file called /etc/X11/xorg.conf it it is a newer version of Redhat. In that file will be horizontal and vertical refresh frequency rates. When you switch monitors, now the entries no longer match the monitor. If this is an older version, the file may be called /etc/X11/XF86Config.
How you fix this is partly up to you. If you have little invested in the installation, the easy way out is to re-install with the new monitor attached.
Some distros, ( not sure if this will work with Redhat ) you can go back through the install process, bypass partitioning, and formatting, and get to the section where the video setup is. Run that only, and exit. I have done that with Mandrake, on some of the older versions.
The third way is to go to the command prompt, and edit the above file, as root user, and put valid values in for the new monitor. The doc for the monitor should specify horizontal and vertical refresh rates. Some makers put that data on their web sites, under Support or Doc links.
Some distros have tools that run from a GUI to adjust the values, but since you can not get a gui running, it would be difficult to use those.