Can't do shortcut--Disk full?

You cannot create shortcuts to an .exe file under C:\Program Files, or C:\Program Files (x86) you can save a shortcut to your Desktop.

As I understand it the target for creating the shortcut is the desktop, exactly as you said.

Told it can't be done here, but can go onto the desktop, click OK. And, that's when I get the message that the disk is full.

Is this a private PC or a works PC?
Are there any disk quotas in play here?
Try the following two methods and report back any success / failure and any error messages received.
Method one : If you open a window to your app (the one you want to create a shortcut for) and right-click, hold and drag to the Desktop you should get a menu to "move, copy, create shortcut here", can you make the shortcut this way?
Method two : Can you right-click the desktop, choose "new shortcut" and browse to the app you want the shortcut to point to?

flycaster said:

Neither worked. ... For method 2, "Paste Shortcut" was greyed out.

The instructions were to choose New shortcut, not paste shortcut.

flycaster said:

New only gives me Folder. Nothing about "new shortcut"

Were you right-clicking on your Desktop? It should work there.

'New' should only be limited to just 'Folder' when you right-click in restricted folders such as the root of the C:\ drive or in 'C:\Program Files'.

You can find the quota information by right-clicking a drive in the This PC (My Computer) on the desktop and choosing properties, quota page. Not sure if it is available on Windows Home though, but unless you have set a quota there should not be any regardless, I was asking just in case this was a works PC that might be shared between employees.
Assuming you tried to create the shortcut the ways I suggested and still no joy and if you have missing options in your context menu then I can only think that either your registry has been altered or is corrupted or certain permissions have been altered to prevent certain actions.
Try running SFC / Scannow from an admin command prompt (find command in the Windows system folder on the start menu, right-click and run as admin).
Once SFC has finished try creating the shortcut again by finding an app or file, right-click, hold, drag to the Desktop and see if you have the "create shortcut here" menu option.
If that fails again we may have to investigate your Windows Defender settings next.