Trust me, that is not the way it should look. Properly operating, the 1901, and in fact most newer LCD today, display almost as well as your Trinitron, so you have something wrong, possibly it is just a DOA monitor. However you don't say what you have done to try to correct the problem, so here are a couple of things you can try if you haven't already. If you have DVI use that connection to run the 1901. Just in case, also make sure you have only one or the other (Analog or DVI) connected to the monitor from the same PC, not both.
Perform a monitor reset from the on screen menu
Perform an auto adjust (hit the + button next to the power button).
If you have XP, enable clear type (use this wizard linked here to do this and to customize your settings)
If none of the above helps, go to your display properties, advanced, settings, and set your color to default setting. Try above again.
Although it sounds like a settings issue, it may also be a driver problem with your video card and you could consider reinstalling or upgrading your driver. For further troubleshooting assistance go the Users Guide for the monitor. Use the Reference tab above to access them.
If you have already done all these things and still no help, contact Dell Support.
Dell Latitude 6430u, w/USB 3.0 dock, Venue 8 Pro Tablet