if I'm not mistaken, it's the version of SDL used by dosbox. Supports full-screen only on the primary monitor.

it's only a few clicks to make your TV the primary monitor before running DOSBox, and reversing this afterwards. Could probably be automated with some clever scripting.

Before I connected the HDMI it worked on both the main laptop's display and on the Dell monitor at the same time so I really never thought I would end up having this problem.

It worked on both monitors at the same time? in fullscreen? That probably means you were using the "clone" option rather than a primary / secondary setup... that would work.

But if it worked with the main display and the VGA monitor first why shouldn't it work with the current configuration? It makes no sense

Probably because the configuration for HDMI is not the same as the one for VGA cables...and Windows is treating it as such...if you configure it to clone as VileRancour said, it will probably work again.

Is not windows, if it were I would never be able to see anything on either display no matter what I would be running and that's not what's going on, as it only happens if one switches BOXDos to full screen.

And it is set to clone the display. Because in reality all that happens when one chooses otherwise is that the display or desktop s extended to the second display so it appears empty. and then one has to manually move whatever application window you want displayed there.

Since there is no way to independently configure DOSBox to use any other display other than the main one in full screen it most likely won't work either.
But i'll try it anyway for argument's sake.

I've configured DOSBox to run in 1024x768 window and if nothing else works that's how i'll use it from now on.

it's just sad that DOSBox cannot use the feature in full screen.

dosbox doesn't do much screen handling on its own. It relies on libsdl for that.
That one has a set of environment variables that you can set. I think some of them might have influence on the multiple monitor behavior.

From your description you haven't set it up to clone but EXTEND your desktop.
When set to clone you see the same apps on both screens. This usually works. The extending usually fails to deliver depending on the program trying to run fullscreen on the second screen

In the case of DOSBox they both fail, I've given up and I'm resorting to making DOSBox work on an OpenGL based 1024x768 window.