Which version of Acrobat?
Are you printing to the same printer in both instances, or is this printer specific rather than computer specific?
If you are using different printers, try swapping them and see if the non-working machine suddenly becomes the working machine.
I have seen this happen before, usually behind images, but sometimes behind a whole document.
If you are using the same printer in all cases, I would get into the print properties on the machine that is printing correctly, and take note of the advanced printing properties. Then, set the non working machine the exact same way.
Sometimes the lesser understood advanced properties can have a huge impact on how the document is handled at the printer.
Hope this helps,
Martin