Couple ideas off the top of my head:

Make sure the 'offending' browser is not Zoomed in, for Firefox it's View -> Zoom -> Reset, for IE it's View -> Text Size -> Medium (I beleive).

With the resolution set at 1024x768,  a skin set to 960/980 wide shouldn't have any issues. If it's in edit mode, it's annoying but you're going to pull your hair out trying to get it look exactly the same, objects are 'blown out' by extra space added and sometimes containers, but you can always click the Edit / View / Design selection in the upper left to get an idea of how things will look when published.

Also, are you using the skins that came with DNN360's package or a different skin with their navigation? I ask because some skins (other than DNN360's included, I think) have a page-width function. I ran into this when using AntsyII, and even though I removed the selector from the skin it would still bring up the page in the 'old' width. I finally purged my cookies and temp files and it began behaving normally. However, I should also note that there was significant editing to the ASCX and CSS in order to get the width correct.

In general, if the problem is only presenting on one computer, it's more likely a problem local to that machine... maybe the browser is a couple versions old, or they have some type of file caching going on perhaps... hard to say without actually seeing the problem.