So if I understand this correctly, the issue comes down to what's happening on the Tabletop, not so much the entire GM interface. When you say you can't switch out maps, are you saying you can't pull down the Page Toolbar to select a different page to load?
Are you able to select images at all or is everything you've placed on the three layers stuck where you've dropped them? Sometimes if you have a large map in the background, you can't actually select the smaller images layered atop it without forcing a deselect of the background map. If there's a possibility of that happening here, try hitting the ESC key to see if you can select any of your other images.
Are you working on the same browser environment when you switch computers? Can the both of you supply me your browser specs .