Lightroom will not open on my desktop.

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

Which version of Lightroom do you use? Lightroom Classic or Lightroom?

Which operationg system do you have installed?

What happened exactly when you start lightroom?

Do you get an error message? If yes, please post the message word-by-word.

If you’re on Lightroom Classic you can try the following:

Reset the Lightroom preferences: How to reset Lightroom Classic preferences

A corrupt LrC catalog can be a cause that Lightroom doesn’t start. Try to restore the catalog from one of the latest backups and check. Or create a new catalog and import several images. Hold the Ctrl-Key while starting LrC. This opens a catalog selection dialog.