Webform module issue - content type not displaying
Drupal can act funny when you start deleting things and then trying to reinstall them. Do you have access to your database?

If so uninstall webform and delete it - then head into your database and delete any webform tables that might still be hanging around. 

Dont even try this without backing up your database first though incase you happen to delete anything important. 

Then re-install webform.

This is a pretty drastic step and you will lose all data surrounding your webforms. 

I have had to do this with other modules that have left tables behind when uninstalled and then they mess when reinstalling said modules. 

Once again though if you take this route be careful what you delete.