Problem solved!  I tried another mouse and keyboard and they work just fine.  I'm not sure why the old ones didn't work but it's not worth chasing it down.  Thanks for your feedback.
My 2011 Dell Studio XPS 7100 desktop was in storage for a couple of years due to a move.  I set it up hoping to copy files from it to a new laptop but can’t get it to do anything. The computer and monitor boot up.  The screen displays a background photo but doesn’t respond to inputs from the wireless mouse or wireless keyboard (new batteries in both).  The screen eventually goes into sleep mode (black screen).  I do get an ‘on indicator’ (green light) on both the keyboard and mouse but they don’t interact with the computer or screen.   When in sleep mode, touching the screen controls on the lower right side of the monitor brings up a window that states the following: “Dell IN2020M.” “There is no signal coming from your computer.” “Press any key on the keyboard or mouse to wake it up.” “To change to another input source, push the monitor button again.”  None of these prompts work. I am able to select ‘auto select’ mode for the video cable, which is either VGA or DVI-D, by using the control buttons on the monitor.  My current cable is a VGA.  I am also able to specify other settings for the monitor, such as brightness, contrast, etc., using the control buttons on the monitor.  I suspect the video cable is functioning or I wouldn’t get the initial background photo on the monitor when the system boots up.  It just won’t move off of that screen. I’m using two VGA cables hooked together for added length.  This is the exact video cable configuration I used prior to storing the computer and it worked fine.  I tried using the individual cables as standalone cables but there was no change.  Any recommended solutions will be greatly appreciated.
Dell Studio XPS 7100 Problem