GeoffMay: I get this with several DOSBox games and it is because the mouse hasn't registered with the DOSBox Window properly. To get round it, I press Alt+Return (puts the DOSBox into windowed format), click in the game to make sure that the mouse is registered properly and then Alt+Return again to put the DOSBox back into full screen mode.

Themken: Try just right clicking on the DOSBox program.

jermungand: At what point? The window (after I've shrunk it) or in some other way?

zandrag: Holding "Ctrl" and hitting F10 toggles DOSBox grabbing control of the mouse and releasing it back to windows.

The only other things I can think of is a corrupt CONFIG.MOO, but reinstalling from GoG should have the correct one.
Or there is some input software, be it mouse or other controller, that may be interfering? By this I mean, some fancy program the device makes you install and sits in the system tray like Logitech stuff that you probably don't actually need.
But, I never saw this be an issue for DOSBox, only DirectX type games.

You can also try running the "Graphic Mode Setup" and change from Overlay to OpenGLnb or DDraw/Direct3D and see if the mouse works.

Themken: Whenever the program is, or looks to be, active. On the active game window, if it is in a window. The other methods mentioned are about doing the same so all should work or none.

townltu: If this is the same issue as it occurs here,
it should help to hit [Alt]+[Enter] 2 times (toggles to window/full screen and back)
Gives my a functioning mouse at 100% success rate.

GeoffMay: Did you get this working with the suggestions?

When this happens to me, I just turn the session into a windowed session, click on it with the mouse until the in game mouse starts responding and then go back to full screen.