I'm guessing that you previously imported the photos into Lightroom, and that's why Lightroom tells you there were no photos found.
Please state the version of Lightroom, your operating system, the camera that took these photos, and whether the photos are JPG or RAW. <== please provide all 4 of these pieces of information.
I am using Windows 10 and Lightroom 6.3. The photos are all JPEG's and were taken with a Sony Powershot. Thank you.
So have you previously imported the photos into Lightroom?
Are the photos dimmed and grayish in the import dialog box?
I have previously imported all of the photos into Lightroom-only 31 of them can be accessed by Lightroom. When I try to import the entire folder with all of the photos again, the ones that are imported/accessible are greyed-out, and the outlines of the remaining 414 photos show as ready to import (the photos themselves don't show, only an outline of them with the jpeg sequential name and a "check" sign indicating that they are selected for import).
So if they have been previously imported, you should not try to import them again, as there is no need to do so.
Just go to the Library Module (not the Import dialog box), find the photos, and make use of them however you'd like.
When I use the File/Open Catalog option in the Library module, I can drill down and select one of the photos that Lightroom will not import after I select "All Files" in the box next to "File name" at the bottom of the Open Catalog command (otherwise I can't see any of the photos). When I click "open", Lightroom asks me if I want to "Relaunch Lightroom with this Catalog?". After clicking "relaunch", Lightroom closes and I get the following message: "Unexpected error opening catalog-the catalog could be opened due to an unexpected error, and the options include "Try Again (which doesn't work), "Choose a Different Catalog" (which takes me back to my external hard drive where I see " no photos in the Current Import) or "Exit" . What do you think? Thanks again.
You are confusing your images (JPG files) with your catalog (LrCat files).
LR does not open individual image files, only catalog files.
Open your catalog (*.LrCat), go to the Library module.
Select a folder or collection on the left, see the images in the grid in the middle.
When I use the File/Open Catalog option in the Library module, I can drill down and select one of the photos that Lightroom will not import after I ...
The instructions to use File->Open Catalog are not what I suggested. This won't solve your problem.
You want to open the catalog normally by double-clicking on the Lightroom icon on your screen, then go to the Library Module and find you photo in the Grid there by using Lightroom's search features to search by file name.