No Driver Selected/Plug-ins disabled/Only External MIDI available in Logic Pro X

Logic can't do anything without an audio interface selected in it's preferences.

Second graphic down from the top, Core Audio Enabled - Input Device:No Driver - Output device:NoDriver

Disable core Audio then re-enable. Try clicking the selection arrows on the right of the Input Device driver selection box, anything available to select? If not, your audio interface has lost connection with the computer, unplug the audio interface, shut the computer down, restart after 15seconds, wait until the computers settles then re-plug the interface and see if Logic responds. All the symptoms are from not having an audio device selected.

But the thing is that you cannot actively select "no driver" and it shouldn't be greyed out. If an interface is missing Logic usually defaults to the System's default device or to Internal IO, both of which seem to be missing here.

Right... I guess Logic does try defaulting to system audio. On my system the up arrow in the driver selection box looked active in the above graphic.

To the original poster, do you have system audio in other applications? If so it could point to a badly corrupted Logic preferences.

Delete user preferences

Before deleting user preferences, note any specific preference settings that you’ve made, and save any custom key commands you've created. Deleting preferences removes any custom preference settings and custom key commands.

To delete the user preferences, do the following:

1. Quit Logic Pro X.
2. In the Finder, choose Go > Go to Folder.
3. Enter ~/Library/Preferences, then click Go.
4. Remove the "com.apple.logic10.plist" file from the Preferences folder. 
5. If you upgraded from an earlier version of Logic Pro, also remove the "com.apple.logic.pro" file.
6. Restart your Mac.

After deleting preferences, restart the computer.

There is also a Logic menu item in the upper Left Logic Pro X menu that allows resetting preferences to default, under the Logic Pro X/Preferences/ menu item.

Yes, that's the menu item I was speaking of, so... what you had was an extremely corrupted Preference file.

Have you checked to see how full your system drive is. If you're running a project on a drive that is neraly full and Logic crashes or even closed normally the preferences can get corrupted.