Wa hoo! I've just read Anubis' FAQ on dosbox and the way to get the game full screen is simply by pressing ALT + ENTER concurrently. To exit, change the screen mode back and press the x in the top corner. Hope that solves your problem.
EDIT:
Eagle of Fire beat me to the punch with some helpful advice. However, here is a link to the specific page for optimising performance.
Optimising
DOUBLE EDIT:
The good news is that Alt + Enter resulted in a frozen screen on my system...which is probably what happened to you, Callum.