I don't think it's the PeopleCode causing the issue because the download works from some computers and not from others with the same user account. The machines which aren't working do not have any extraneous toolbars (Yahoo, Google, etc.) which would block popups and I have turned the IE 7 popup blocker off completely. The site is listed as a trusted site, Active X is set to enable all downloads, they have the same add-ons enabled, and I've even gone so far as to check EVERY Internet Option setting is the same as it is on the working computer. I've checked that both machines are running the same version of IE 7 and have the same Java version running and still no solution.
On a whim, I downloaded Firefox to see if that would give me any clues and found that if I had the popup blocker enabled and told it to allow popups from that site, it gave me the same error, but if I disabled the popup blocker and deleted the site from allowed popup sites, it would work. Unfortunately, Firefox isn't an officially supported browser for our version of PeopleSoft so I can't just tell the users to install and use that instead.