One of my users had a similar. After checking for much more complicated solutions including shortcut commands, I found out they were going to the wrong address.
What had happened? Well OWA as far as I can tell uses frames. One of the features of frames is that you can link directly to a frame. My user had created the bookmark that linked to their specific viewing pane frame and not to the full page. Deleting the bookmark and replacing it with one that pointed to the correct address solved their problem.
What should you do? Check to see if the address you reach is the same from both the computer OWA works from and the one that OWA doesn't. If they don't match, delete any bookmarks to the wrong address and replace it with the one that does. In my case the non-working address included my user's username. The correct address was of the form http://www.domain.com:portnumber/exchange/.
I'm sorry my answer couldn't come close to the time you asked it. Considering this is the top Google result for this issue, I hope others might use it. Especially since most other answers refer to Outlook and not Outlook Web Access (OWA). Our version I believe is 2003.