Theoretically you shouldn't be able to resize the window; it's set at 800 x 600. However, there's a bug in some versions of Windows that sometimes lets you change it, with the result you've found - the mouse doesn't work properly. Closing the game and reopening it will return the window to the proper size.
It is possible to move about the screen using keyboard controls, but you still need the mouse to do things like picking up a peep. I don't have the game installed on this machine, but if you go to the Menu screen, then click on Help I think there's a description of the keyboard shortcuts.
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To err is human; to arr is pirate.