Which version of Lightroom were you using on the crashed system? And which version of Lightroom have you installed on the desktop. There are two current versions of Lightroom: one called Lightroom Classic (which is the latest iteration of the traditional version that has been in existence for over 12 years, and uses locally stored images), the other is now simply called Lightroom (introduced 3 years ago, now up to version 3.4, and the images are stored in the cloud). Or you may have been using an older version of the traditional Lightroom, such as LR5 or LR6. We just need to know which you were using if we are to offer any help with the issue, as the recovery scenarios are completely different.