Based on the information provided, it is defiantly something specific to the IE settings on this particular computer.
here are a few additional things to try:
-Clear the browsers cache and delete any saved cookies.
-In IE, click the Tools menu (Icon of a gear in the top right corner) and select Internet Options. On the Privacy tab, click the Advanced button, Check the "Override automatic cookie handling" box, and check the "Always Allow session cookies" box.
- Still on the Privacy tab, click the sites button, have them add your domain to the always allow list
- On the security tab, select Trusted Sites, then click the Sites button and add your domain to the Trusted Sites list. Select restricted sites, and make sure your domain is not on the restricted sites list.