When running the update script on a new a new installation of Drupal version 6.20, I was getting this:
<!--[if lt IE 7]--> Fatal error: Call to undefined function phptemplate_get_ie_styles() in htdocs/themes/garland/maintenance-page.tpl.php on line 23
The problem turned out be that the .info file was missing for the Minnelli theme, and that's the default theme for the maintenance page. I'm not sure how it went missing, but I just copied minnelli.info from a different Drupal installation into the themes/garland/minnelli/ directory and all was well.