Hello Ernie and welcome to Seven Forums.
There may be a problem with the device driver for the monitor. If you know the brand and model for the monitor that's not working, go to the manufacturer's website and see if they have a newer driver available for Windows 7. (You may find 2 different drivers - a 32-bit driver and a 64-bit driver.
Choose the one for your computer.) You'll probably have to search for a link called "support and downloads" or "driver downloads" or something similar. Also on that same website you'll probably see a troubleshooting section with some suggested fixes.
Just as an example, this is the HP site:
HP Support & Drivers | United States
With the non-working monitor plugged in to the computer, you could also open the Windows 7 Device Manager. See if there are any yellow or red warnings/errors showing for the monitor.
How Do I Open Device Manager in Windows 7?
If you do have any warnings/errors, this previous Forum thread explains the best way to update the driver.
Best way to update drivers for free?