It looks like this is due to the TitleKey extension being installed but its index table not being fleshed out. With the index entries missing, OpenSearch suggestions are returned empty and the drop-down box doesn't get displayed.

Run this script on the prototype wikis to rebuild the title indexes:
extensions/TitleKey/rebuildTitleKeys.php

Version: unspecified
Severity: enhancement
URL: http://prototype.wikimedia.org/en.wikipedia.org/Main_Page