White screen of death after failing on plugin install

I've tried to install the W3 cache plugin but during the activation it started to file because of permissions. I changed the permissions to make W3 cache plugin working. After I run the plugin test case I got the white screen of death.

I was not able to get back inside my admin panel or else so I deleted W3 cache plugin files and removed the inserted tags in config and .htacccess.

Now I am able to get back into the admin but everything seems to be damaged. No plugins are working and I get the follow message on the plugin page;

The plugin contact-form-7/wp-contact-form-7.php has been deactivated due to an error: Plugin file does not exist.
The plugin easy-digital-downloads/easy-digital-downloads.php has been deactivated due to an error: Plugin file does not exist.
The plugin nextgen-gallery/nggallery.php has been deactivated due to an error: Plugin file does not exist.
The plugin pronamic-ideal/pronamic-ideal.php has been deactivated due to an error: Plugin file does not exist.
The plugin w3-total-cache/w3-total-cache.php has been deactivated due to an error: Plugin file does not exist.
The plugin wp-smushit/wp-smushit.php has been deactivated due to an error: Plugin file does not exist.

What can I do to fix this issue? Where should I look, what actions can I perform to get this fixed.

Many Thanks!