There's lots of things you can try, although what you have said does indicate a firewall problem. Unfortunately I'm not all that familiar with Zone Alarm, but the first thing I would check is that IE is enabled in the Applications list. You have to make sure that the SSL port (port 443) is open, but if IE is 'allowed', this should be open by default. One way to fix any uncertainties might be to completely remove and reinstall ZA, which should hopefully reset everything to defaults, and then she will have all the pop-ups again, asking to allow this and that. Oh, by the way, is she using a router (with a firewall) or an ADSL modem?
She could also try clearing the cache and cookies in IE, which often works wonders.
There is another quick fix, and that would be to get her to install another browser, such as Firefox. Hopefully that would work 'out of the box', until such time as you can get round to sorting out IE.
Just one more thing - don't have ZA and Windows Firewall on simultaneously, as this can cause problems.