Have you checked if that generic computer has the newest version of Tableau Reader (compatible with your Tableau Desktop version)?
Just recently I had the same problem with blank worksheets in Reader and updating program to the newest version helped.
...and I wouldn't rule out a driver problem quite yet. It could be Excel is opening the .cub file with a different version of the SQL Analysis Services driver than the one available (or not) to Tableau.
It could be instructive to open the latest log.txt file in \My Documents\My Tableau Repository\Logs folder to see if there are complaints about a driver or some other issue. I'd recommend you clear out the contents of this folder before you open Reader and the TWBX so you have a single, small file to peek at.
Thanks all for the help! Sorry for the delay (I was on a nice long vacation!)
We were able to determine that it was actually a driver problem! (Kudos Russell) It turned out that I was running Excel 2010 when creating the offline cube, where as our other machines were still on 2007. We installed:
Microsoft Core XML Services (MSXML) 6.0 SP 1
Microsoft SQL Server 2008 R2 Analysis Services OLE DB Provider
And things started working fine!
Thanks for the suggestion for looking into the log which helped us locate the driver issue!