What can I do to fix missing start menu/desktop icons for a domain user?

Her profile is corrupt, period. How it happened is a bit of an interesting mystery, but the fix is the same. Delete/recreate her profile and copy all of her stuff back over.

My guess is that somehow the winlogon process got really confused somehow and set her profile directories (desktop, start menu, etc.) to the All Users profile. As far as her being authenticated to the network, that just can't have happened unless she did get her password right at some point and winlogon was lying to her about it. Either that, or the shares she had access to have the everyone permission set.

Like I said, interesting mystery. But I'm betting if she signed into a different computer everything would work correctly.