Can somebody clarify the following for me?

My X server has fatal errors, and the display resolution needs to be reset to the original value.

The file /etc/X11/xorg.conf therein defines the display modes for the monitor, but does not appear to determine which one of the monitor resolutions has been selected to use.

What file/path exactly determines which of the possible monitor resolutions has been selected for use?

The file is /etc/X11/xorg.conf if you're using Xorg. On XFree86 it's something like /etc/X11/XF86Config or perhaps the same with -4 added to the tail. Anyway, that's the file; and as you said, the resolutions are defined there, in the form of

"1024x768" "800x600" "640x480"

and so on. There are probably multiple lines, one line per one colour depth, but you should understand that. The way those lines are read is: the selected colour depth determines which one of the lines is used. In that line the first one from the left (above it's "1024x768") is the "default" one, i.e. the one that is first tried to be used. If it cannot be used for some reason (card or driver not supporting it or something), then the next one is tried and so on until a suitable one is found or the list ends. This is what the man page says about it too, I think.

Two other important things are 1) vertical and horizontal refresh rates; these must match your screen, if defined -- wrong values may result in error or even damage something if you've got bad luck.. and 2) colour depth; use the colour depth you need, and one that is supported. All these are configured in the xorg.conf file, in the sections for Monitor, Screen and even Device (video card).

After this you may have somekind of script that is read when X starts that tries to change the resolution; that's beyond X then. You should test the resolution with
which should start just X with xterm, with the desired resolution.

You should have a default mode that tells which bit to use as the default, there it should provide the different resolution modes that it uses, the first one listed in the line is the default it will use.

I edited the xorg.conf file until the server worked again based upon your advice. It is not clear to me why, but the error stated the refresh rates were at fault for some of the display settings. Nor was I aware that the order of the display settings established the default setting for the monitor. Anyway, everything is working perfectly now. Thanks again for the assistance.