What version of the Web Adaptor are you using? What version of IIS? Is IIS used for anything else other than this one web adaptor? Are you using a default instance of IIS, or what customisation have you done?
If it's 11.x onwards, have you installed all the pre-requisites:
https://enterprise.arcgis.com/en/system-requirements/11.1/windows/arcgis-web-adaptor-system-requirem...
and in the right order:
https://enterprise.arcgis.com/en/system-requirements/11.1/windows/arcgis-web-adaptor-system-requirem....
Sorry to ask so many question, searching for a 500.19 error on Google leads to a multitude of errors on the IIS rather than Esri side, so we need to try and narrow things down quite a bit.
Scott Tansley
https://www.linkedin.com/in/scotttansley/