Lightroom will not open on my desktop

Unfortunately you haven't given us detailed infos about your issue and any information about your system. Therefore, all proposed solutions are a look into the crystal ball

What do you have done on your system before the error occur?

Please provide a copy of your 'System Info'. This can be get from the Lightroom menu item Help > System Info. There's a copy button in the System Info dialog. Press this button and paste the info into your next forum post.

On a first step try to reset the preferences of LrC manually:  How to reset Lightroom Classic preferences (adobe.com)

It's recommended to backup your preferences before you reset the preferences:  https://helpx.adobe.com/lightroom-classic/kb/preference-file-and-other-file-locations.html

If this doesn’t help the next step is to switch off the GPU support from the Lightroom preferences and check if that helps to fix the issue. If Lightroom doesn't start correctly the please see "Solution 2" in the document behind the link below.

Troubleshoot GPU issues | Lightroom Classic (adobe.com)

If it's help see here Troubleshoot GPU issues | Lightroom Classic (adobe.com) and check the different steps.

If this also doesn’t perhaps a issue with your catalog. Restore the catalog from a recent backup -> Disaster strikes - a corrupted catalog! | The Lightroom Queen

Or create a new catalog and import several images. Hold the Ctrl-Key while starting LrC. This opens a catalog selection dialog.

Click on “Create a New Catalog” to create a new one and see if this catalog works. If yes, you could then try to import your current catalog into the new one.

Alternatively, you can rename the appropriate catalog folder like foldername.sav and the restart Lightroom.