Why is OS 10.13.3 file > "new folder" grayed out.

Navigate to your Home/Desktop/ folder. Press Command-I to open the Get Info window. At the bottom is the permissions panel. Take a screenshot and post here. Then navigate to the Users folder at the root of the drive. Select the Home folder and do the same.

To Post A Screen Shot

1. Press Command-Shift-4 which will change the cursor to crosshairs.
2. Hold down the mouse button and use the crosshairs to select the part of the screen you wish to capture.
3. Release the mouse button and the image will be saved to your Desktop.
4. Drag the pic into your open forum editor. If that fails then go to the following steps.
5. Click on the Camera icon in the toolbar of the forum message editor.
6. Drag the image onto the Choose File button and click on the Insert button.

I'd guess you have a permissions problem. The following should help:

Repair Home Folder Permissions

Resolve issues caused by changing the permissions of items in your home folder

Your Home folder permissions are not correct. Here is what I have on my system:

You might try the following to fix this.

Repair Permissions for Home Folder

Boot into Single-user Mode, then enter each command line. Press RETURN after each:

chmod -R -N /Users/username

chown -R root:wheel /Users/username

chmod -R 600 /Users/username

After each command has been run restart the computer by entering:

reboot

Press RETURN.

Check results to be sure they match what is seen on mine.