Try having Windows reinstall the driver for the monitor itself. Sounds like that could be an issue. If Windows is not recognizing the resolution capability of the monitor, that's usually the issue.
The ASUS MS238H should have 1920x1080 resolution as a max. You might also see if the monitor came with a CD with any type of drivers on it (usually Windows should figure it out by itself though).
Are you connected with DVI or HDMI? Those would be the preferred connection types for a 1080p monitor.