Classic Lightroom wont lauch

Ah, I missed that the files were on the desktop, despite being in plain site!

Now re-looking at that, I now notice on two of the files, a small cloud icon apparently associated, is some sort of cloud sync going in?

In LrC, click on Help, then System Info, note the info about library path. Can you post in a reply that info?

In a first step try to reset the preferences to the default settings by doing the following steps:

• Close Lightroom.
• Windows: Hold down [Alt]+[Shift] while restarting Lightroom.
• Overwrite the Preferences when prompted by the dialog.
• Close Lightroom.
• Restart Lightroom.

It's recommended to backup your preferences before you reset the preferences to the default settings: 

https://helpx.adobe.com/lightroom-classic/kb/preference-file-and-other-file-locations.html

The next is to try the following steps:

• Close Lightroom
• Backup the folder : C:\Users\xxxx\AppData\Roaming\Adobe\Lightroom to a save location and then rename it to LightroomOld
• Restart Lightroom

Another try is to hold the Ctrl-Key while starting LrC. This opens a catalog selection dialog.

Select the appropriate catalog and let check it – note the checkmark to check its integrity. If that does not help, try to create a new one and see if this catalog then works. You could then try to import your current catalog into the new one.

If this already doesn't help, provide a copy of your 'System Info'. This can be get from the LrC Help > System Info menu item. There's a copy button in the System Info dialog. Press this button and paste the info into your next forum post.

What has been changesd on your system before the issue occur?