I am now at the proper resolution...
A couple of updates.
I read on a different forum that someone had successs trying "Generic PnP Monitor" for the
driver for this monitor. I changed it and rebooted, and was still unable to see the proper resolution.
I then looked in the Monitor Properties of the Catalyst Control Center (CCC) I was able to deselect the option to "Use Extended Display Identification Data (EDID) or
driver defaults" and set Maximum Resolution to 1680x1050.
I rebooted, and tried setting the resolution again from the desktop and it still didn't show the right resolution choice.
I then went to CCC in the DeskTop Properties and was able to select 1680x1050. This did the trick!
I can now see 1680x1050 on the selection on the desktop as well.
Just for information, I am currently staying with my VGA cable.
In case someone searches for DVI and finds this thread, my card is DVI-I and my monitor is DVI-D. I was able to confirm by searching that to connect the two you can use a DVI-D cable. This is also a good option if you want to force DVI-I to use Digital (DVI-I is digital and analog) using a DVI-D cable forces it to use digital by not passing the analog wires through.