When I start Ubuntu 18.04 (kubuntu) I can use konqueror either by clicking it in my favorites, or another part of the menu tree. Alternatively I have typed konqueror in yakuake (terminal) and used konqueror that way. After using konqueror and properly closing konqueror, I can then TRY to run konqueror again later, however konqueror does NOT run. It will not run from terminal or kmenu.

I tried going to the terminal to run konqueror a second time, however typing konqueror and pressing enter does nothing. when I type "konqueror" followed by enter I expect to the some form of verbose response from konqueror as I have seen in the past. I however get absolutely NO response. Typing konqueror into the terminal only causes the cursor to temporarily disappearing as it would do when ANY program is executed from the terminal, however after a moments delay, a new line appears and the standard prompt returns to my terminal with a nice blinking cursor is once more present. No error messages are displayed, and konqueror does not run.

if I check the computer the next morning, or hours later konqueror has still not started and typing into the terminal or clicking konqueror in kmenu produces NO result.

After a restart of the computer, konqueror will run on clicking kmenu or from terminal. Once again after a reboot, if I close konqueror it will not run a second time. I can however start separate instances of konqueror IF I do not quit/shutdown the first instance. Once the last instance of konqueror is closed however konqueror will not restart, or produce an error even when typed from the terminal. (Any terminal including konsole)

After the last instance of konqueror was closed, is it possibly still running in the background? To check that you can use Ctrl+Esc to bring up the process list and then filter to "konqueror".
If it is in fact still running in the background you can try killing the process by right-clicking on the entry in the process list and select End Process and then try launching it again.

There was another complaint here recently about konqueror's behavior. I'd recommend filing a ticket to bugs.kde.org to get the problem fixed.