If a page renders differently for a site administrator than for an unprivileged user, you likely have files that have been modified or checked in, but not published.
For display issues, it's probably your CSS file. Find any CSS files linked to the page and republish. Default file location is in
If whole page elements are not displaying, you likely haven't published the page itself. When viewed as the site admin, you'll get one of two messages:
Either way, you need to publish the page. It's unlikely you have a rights/permissions issue, since you have already given the second user full control.
Another thing: if it only happens on one computer, it could be a browser caching issue. Try force refreshing the page (in Internet Explorer, do Ctrl + F5). This will force the browser to ignore cached images and elements when reloading. Alternately, you could clear the browser's cache and cookies.