Laptop and external monitors go black when I close the laptop

You need to change some of your "power" settings.  Specifically, what actions to take on the power-button, sleep button, and lid closing events.

This is found in Control Panel -> Power -> Advanced Power -> Choose What the Power Button Do.   At that screen change the "When I close the lid" to "Do nothing".   I believe the default is to "Sleep" the system.  The power control can also be accessed via the "Settings Applet (looks like a gear for icon) ->  System -> Power & Sleep -> Additional Power Settings -> Choose What the Power Button Do -> "When I close the lid".  And again, you can switch it to "Do nothing".   You need to make this election for both On battery and Plugged in.   In your case, you may only want to change the "Plugged In" option, and you may want to leave  the "on Battery" option set to "Sleep" so that closing the lid when undocked and on battery will "Sleep the computer".

While there, you may also want to adjust what the power button and sleep button.  If your laptop has an explicit sleep button, some people want the power button to perform a shutdown (power off), and some people want the power button to perform a "Sleep to standby power".   Your choice.

I appreciate the help, but it doesn't seem to apply to Windows 10, ( or maybe it's my laptop that's the problem.) There is no "Power" setting in the control panel. Also, nowhere can I find the "chose what the Power Button does" selection.