Found the culprit which blocked the search-index beeing build. The node 8633 created 2014-07-04 15:08:42 +0200 by admin contained php-code which lead to an php-error. Since that date the search-index hasn't been properly setup.
I've deleted that node.
I've setup a cron job on the Linux server to run every 5 minutes to rebuild the index. That will take a few hours to be done.
After the rebuild is done I'll change the cron job to run every 30 minutes. that will be sufficient for this page.
After about 75% of indexing an error showed up, that the entered date was to big for a tablefield in table search_dataset. Field data of type text could only hold 64k of data which in this case wasn't sufficient.
Changed field data in table search_dataset from text to mediumtext which can hold about 16MB of data. After that change indexing continued.