that is a bit odd. I never heard of this problem.
Which version of dosbox are you using ?

Yeah, works fine for me using the attached script(s) to run & install the shareware version.

I'm using DOSBox 0.72. When I downloaded and ran the game Castle Adventure, it runs in a little window, so I can play it although it's small. But when I tell it to play full screen in the properties, it's "split screen" too.

So it only happens when you switch to fullscreen?? Please post
the full specs of your system and complete information about
the problem next time.
Maybe your monitor has some buttons to move the screen to
adjust for the bad placement.

Have you changed DOSBox configuration in some way? If not, try editting dosbox.conf and change output=surface to output=ddraw.

And updating your videocard drivers to the latest version wouldn't hurt. It's amazing how many people still use the ones shipped with their cards, they can be many months old

If you've set fulldouble=true and aspect=true, try setting either one or both to false. That particular combination (both true) corrupts Dosbox fullscreen graphics on my laptop with an S3 video chip.